Statistical and thermal physics: With computer applications

Statistical and Thermal Physics: With Computer Applications

Volumn , Issue , 2010, Pages

  Gould, Harvey ^a   Tobochnik, Jan ^a  

^a NONE

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EID: 80555152446     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Book

References (215)

1. P. W. Atkins, The Second Law, Scientific American Books (1984). A qualitative introduction to the second law of thermodynamics and its implications.
2. Manfred Eigen and Ruthild Winkler, How the Principles of Nature Govern Chance, Princeton University Press (1993).
3. Richard Feynman, R. B. Leighton, and M. Sands, Feynman Lectures on Physics, Addison- Wesley (1964). Volume 1 has a very good discussion of the nature of energy and work.
4. Martin Goldstein and Inge F. Goldstein, The Refrigerator and the Universe, Harvard University Press (1993).
5. Harvey Gould, Jan Tobochnik, and Wolfgang Christian, An Introduction to Computer Simulation Methods, 3rd ed., Addison-Wesley (2006).
6. J. G. Oliveira and A.-L. Barabási, "Darwin and Einstein correspondence patterns," Nature 437, 1251 (2005). The authors find that the probability that Darwin and Einstein responded to a letter in t days is well approximated by a power law, P(t ) ~ t -a with a ~ 3/2. How long does it take you to respond to an email?
7. Jeremy Rifkin, Entropy: A New World View, Bantam Books (1980). Although this book raises some important issues, like many other popular books and articles, it misuses the concept of entropy. For more discussion on the meaning of entropy and how it should be introduced, see and .
8. Robert H. Romer, "Heat is not a noun," Am. J. Phys. 69(2), 107-109 (2001).
9. See also Art Hobson, "The language of physics," Am. J. Phys. 69(6), 634 (2001)
10. David T. Brookes and Eugenia Etkina, "Using conceptual metaphor and functional grammar to explore how language used in physics affects student learning," Phys. Rev. ST Phys. Educ. Res. 3(1), 010105-1-16 (2007).
11. A listing of many of the textbooks on statistical mechanics and thermodynamics can be found at . Some of our favorites are listed in the following. It is a good idea to look at several books while you are learning a subject for the first time. Sometimes the same argument with slightly different wording can seem clearer.
12. Daniel J. Amit and Yosef Verbin, Statistical Physics, World Scientific (1999).
13. Ralph Baierlein, Thermal Physics, Cambridge University Press (1999).
14. Stephen Blundell and Katherine Blundell, Thermal Physics, 2nd ed., Oxford University Press (2006).
15. Craig F. Bohren and Bruce A. Albrecht, Atmospheric Thermodynamics, Oxford University Press (1998).
16. John J. Brehm and William J. Mullin, Introduction to the Structure of Matter, John Wiley & Sons (1989).
17. Debashish Chowdhury and Dietrich Stauffer, Principles of Equilibrium Statistical Mechanics, Wiley-VCH (2000). This text is more advanced than ours, but contains many accessible gems.
18. F. Mandl, Statistical Physics, 2nd ed., John Wiley & Sons (1988).
19. F. Reif, Statistical Physics, Vol. 5 of the Berkeley Physics Series. McGraw-Hill (1967). This text was probably the first to make use of computer simulations to explain some of the basic properties of macroscopic systems.
20. F. Reif, Fundamentals of Statistical and Thermal Physics, McGraw-Hill (1965). Our presentation owes a large debt to the two books by Reif on statistical physics.
21. Daniel V. Schroeder, An Introduction to Thermal Physics, Addison-Wesley (2000). Schroeder's text has many interesting applications.
22. C. J. Adkins, Equilibrium Thermodynamics, 3rd ed., Cambridge University Press (1983).
23. Ralph Baierlein, Thermal Physics, Cambridge University Press (1999).
24. Robert P. Bauman, Modern Thermodynamics with Statistical Mechanics, Macmillan Publishing Company (1992).
25. Stephen J. Blundell and Katherine M. Blundell, Thermal Physics, 2nd ed., Oxford University Press (2009).
26. Craig F. Bohren and Bruce A. Albrecht, Atmospheric Thermodynamics, Oxford University Press (1998). A book that should be read by professors and students alike. In particular, they discuss the history of the ideal gas pressure equation of state and why Charles deserves none of the credit. This chapter has been influenced by their discussion of thermodynamics.
27. Herbert B. Callen, Thermodynamics and an Introduction to Thermostatistics, 2nd ed., John Wiley&Sons (1985). Callen's discussion of the principles of thermodynamics is an example of clarity.
28. Debashish Chowdhury and Dietrich Stauffer, Principles of Equilibrium Statistical Mechanics, VCH (2000).
29. J. S. Dugdale, Entropy and its Physical Meaning, Taylor & Francis (1996). An accessible introduction to thermodynamics.
30. Harvey S. Leff and William D. Teeters, "EER, COP, and the second law efficiency for air conditioners," Am. J. Phys. 46, 19-22 (1978).
31. Don S. Lemons, Mere Thermodynamics, Johns Hopkins University Press (2009). Highly recommended.
32. Beth Lindsey, Paula Heron, and Peter Shaffer, "Student ability to apply the concepts of work and energy to extended systems," Am. J. Phys. 77, 999-1009 (2009). This paper inspired our Example 2.2.
33. Michael E. Loverude, Christian H. Kautz, and Paula R. L. Henon, "Student understanding of the first law of thermodynamics: Relating work to the adiabatic compression of an ideal gas," Am. J. Phys. 70, 137-148 (2002).
34. Alan Macdonald, "A new statement of the second law of thermodynamics," Am. J. Phys. 63, 1122-1127 (1995).
35. F. Mandl, Statistical Physics, 2nd ed., John Wiley & Sons (1988).
36. David E. Meltzer, "Investigation of students' reasoning regarding heat, work, and the first law of thermodynamics in an introductory calculus-based general physics course," Am. J. Phys. 72, 1432-1446 (2004).
37. Barry R. Parker and Robert J. McLeod, "Black hole thermodynamics in an undergraduate thermodynamics course," Am. J. Phys. 48, 1066-1070 (1980).
38. F. Reif, Statistical Physics, Vol. 5 of the Berkeley Physics Series, McGraw-Hill (1965).
39. Wayne Saslow, "An economic analogy to thermodynamics," Am. J. Phys. 67, 1239-1247 (1999). The author develops several analogies between economic systems and thermodynamics.
40. Daniel V. Schroeder, An Introduction to Thermal Physics, Addison-Wesley (2000).
41. Daniel F. Styer, "A thermodynamic derivative means an experiment," Am. J. Phys. 67, 1094-1095 (1999).
42. Mark W. Zemansky and Richard H. Dittman, Heat and Thermodynamics, 6th ed., McGraw- Hill (1981). A classic text on thermodynamics.
43. R.K.P. Zia, Edward F. Redish, and Susan R. McKay, "Making sense of the Legendre transform," Am. J. Phys. 77, 614-622 (2009).
44. The history of thermodynamics and statistical mechanics is fascinating and not one to which we can do justice. We encourage you to read some of the original sources such as the English translation of Sadi Carnot's paper in Reflections on the Motive Power of Fire: A Critical Edition with the Surviving Scientific Manuscripts, edited by Robert Fox, Manchester University Press (1986). Other recommended books are listed in the following.
45. Stephen G. Brush, The Kind of Motion We Call Heat: A History of the Kinetic Theory of Gases in the Nineteenth Century, Elsevier Science (1976).
46. See also The Kind of Motion We Call Heat: Physics and the Atomists, Elsevier Science, Amsterdam (1986)
47. The Kind of MotionWe Call Heat: Statistical Physics and Irreversible Processes. Elsevier Science (1986).
48. Hasok Chang, Inventing Temperature, Oxford University Press (2004). An interesting synthesis on the history of the concept of temperature.
49. E. Garber, S. G. Brush, and C.W.F. Everitt, eds., Maxwell on Heat and Statistical Mechanics, Lehigh University Press (1995).
50. Peter M. Harman, Energy, Force, and Matter, Cambridge University Press (1982).
51. Martin J. Klein, "Thermodynamics in Einstein's thought," Science 157, 509-516 (1967)
52. "Maxwell, his demon, and the second law of thermodynamics," Am. Scientist 58, 84-97 (1970)
53. "Carnot's contribution to thermodynamics," Physics Today 27(8), 23-28 (1974).
54. Thomas S. Kuhn, "Energy conservation an example of simultaneous discovery," 321-356 in Critical Problems in the History of Science, edited by Marshall Clagett, University of Wisconsin Press (1959).
55. Robert D. Purrington, Physics in the Nineteenth Century, Rutgers University Press (1997). This monograph discusses the rich and fascinating history of thermodynamics among other developments.
56. Daniel M. Siegel, "The energy concept: A historical overview," Materials and Society 7, 411-424 (1983).
57. Crosbie Smith, The Science of Energy: A Cultural History of Energy Physics in Victorian Britain, University of Chicago Press (1998).
58. Vinay Ambegaokar, Reasoning About Luck, Cambridge University Press (1996). A book developed for a course for nonscience majors. An excellent introduction to statistical reasoning and its uses in physics.
59. Ralph Baierlein, Atoms and Information Theory, W. H. Freeman (1971). The author derives the Boltzmann distribution using arguments similar to those used to obtain (3.168). Arieh Ben-Naim, Entropy Demystified: The Second Law Reduced to Plain Common Sense, World Scientific (2007).
60. Deborah J. Bennett, Randomness, Harvard University Press (1998).
61. Peter L. Bernstein, Against the Gods: The Remarkable Story of Risk, John Wiley & Sons (1996). The author is a successful investor and an excellent writer. The book includes an excellent summary of the history of probability.
62. David S. Betts and Roy E. Turner, Introductory Statistical Mechanics, Addison-Wesley (1992). Section 3.4 is based in part on Chapter 3 of this text.
63. Jean-Phillippe Bouchaud and Marc Potters, Theory of Financial Risks, Cambridge University Press (2000). This book by two physicists is an example of the application of concepts in probability and statistical mechanics to finance. Although the treatment is at the graduate level and assumes some background in finance, the first several chapters are a good read for students who are interested in the overlap of physics, finance, and economics. Also see J. Doyne Farmer, Martin Shubik, and Eric Smith, Vinay Ambegaokar, Reasoning About Luck, Cambridge University Press (1996). A book developed for a course for nonscience majors. An excellent introduction to statistical reasoning and its uses in physics.
64. Ralph Baierlein, Atoms and Information Theory, W. H. Freeman (1971). The author derives the Boltzmann distribution using arguments similar to those used to obtain (3.168). Arieh Ben-Naim, Entropy Demystified: The Second Law Reduced to Plain Common Sense, World Scientific (2007).
65. Deborah J. Bennett, Randomness, Harvard University Press (1998).
66. Peter L. Bernstein, Against the Gods: The Remarkable Story of Risk, John Wiley & Sons (1996). The author is a successful investor and an excellent writer. The book includes an excellent summary of the history of probability.
67. David S. Betts and Roy E. Turner, Introductory Statistical Mechanics, Addison-Wesley (1992). Section 3.4 is based in part on Chapter 3 of this text.
68. Jean-Phillippe Bouchaud and Marc Potters, Theory of Financial Risks, Cambridge University Press (2000). This book by two physicists is an example of the application of concepts in probability and statistical mechanics to finance. Although the treatment is at the graduate level and assumes some background in finance, the first several chapters are a good read for students who are interested in the overlap of physics, finance, and economics. Also see J. Doyne Farmer, Martin Shubik, and Eric Smith, "Is economics the next physical science?," Phys. Today 58(9), 37-42 (2005). A related book on the importance of rare events is by Nassim Nicholas Taleb, The Black Swan: The Impact of the Highly Improbable, Random House (2007).
69. Wolfgang Christian and Anne Cox. See to download a simulation of the Galton board. Other simulations related to statistical and thermal physics are also available at this site.
70. Giulio D'Agostini, "Teaching statistics in the physics curriculum: Unifying and clarifying role of subjective probability," Am. J. Phys. 67, 1260-1268 (1999). The author, whose main research interest is in particle physics, discusses subjective probability and Bayes' theorem. Section 3.4 is based in part on this article.
71. F. N. David, Games, Gods and Gambling: A History of Probability and Statistical Ideas, Dover Publications (1998).
72. Marta C. González, César A. Hidalgo, and Albert-László Barabási, "Understanding individual human mobility patterns," Nature 453, 779-782 (2008). The authors studied the trajectories of 100,000 cell phone users over a six-month period and found that human trajectories cannot be simply modeled by a Lévy flight or as an ordinary random walk. Similar studies have been done on animal trajectories. The website has many examples of the application of probability to diverse systems of interest in statistical physics.
73. T.P. Hill, "The first digit phenomenon," Am. Sci. 86, 358-363 (1998).
74. James R. Huddle, "A note on Benford's law," Math. Comput. Educ. 31, 66 (1997).
75. Gene F. Mazenko, Equilibrium Statistical Mechanics, John Wiley &Sons (2000). Sections 1.7 and 1.8 of this graduate level text discuss the functional form of the missing information.
76. Leonard Mlodinow, The Drunkard'sWalk: How Randomness Rules Our Lives, Vintage Press (2009). A popular book on how the mathematical laws of randomness affect our lives.
77. Elliott W. Montroll and Wade W. Badger, Introduction to Quantitative Aspects of Social Phenomena, Gordon and Breach (1974). The applications of probability that are discussed include traffic flow, income distributions, floods, and the stock market.
78. Elliott W. Montroll and Michael F. Shlesinger, "On the wonderful world of random walks," in Studies in Statistical Mechanics, Vol. XI of Nonequilibrium Phenomena II, edited by J. L. Lebowitz and E. W. Montroll, North-Holland (1984). An excellent article on the history of random walks.
79. Joáo Gama Oliveira and Albert-László Barabási, "Darwin and Einstein correspondence patterns," Nature 437, 1251 (2005).
80. Richard Perline, "Zipf's law, the central limit theorem, and the random division of the unit interval," Phys. Rev. E 54, 220-223 (1996).
81. The outcome of tossing a coin is not really random. See Ivars Peterson, "Heads or tails?," Science News Online, and Erica
82. Klarreich, "Toss out the toss-up: Bias in heads-or-tails," Science News 165(9), 131 (2004), .
83. Some of the original publications include Joseph Ford, "How random is a coin toss?," Phys. Today 36(4), 40-47 (1983)
84. Joseph B. Keller, "The probability of heads," Am. Math. Monthly 93, 191-197 (1986); and Vladimir Z. Vulovic and Richard E. Prange, "Randomness of a true coin toss," Phys. Rev. A 33, 576-582 (1986).
85. Vladimir Z. Vulovic and Richard E. Prange, "Randomness of a true coin toss," Phys. Rev. A 33, 576-582 (1986).
86. S. Redner, "Random multiplicative processes: An elementary tutorial," Am. J. Phys. 58, 267- 273 (1990).
87. Jason Rosenhouse, The Monty Hall Problem: The Remarkable Story of Math's Most Contentious Brain Teaser, Oxford University Press (2009).
88. Charles Ruhla, The Physics of Chance, Oxford University Press (1992).
89. B. Schmittmann and R. K. P. Zia, "'Weather' records: Musings on cold days after a long hot Indian summer," Am. J. Phys. 67, 1269-1276 (1999). A relatively simple introduction to the statistics of extreme values. Suppose that somebody breaks the record for the 100m dash. How long do such records typically survive before they are broken?
90. Kyle Siegrist at the University of Alabama in Huntsville has developed many applets to illustrate concepts in probability and statistics. See and follow the link to Bernoulli processes.
91. J. Torres, S. Fernández, A. Gamero, and A Sola, "How do numbers begin? (The first digit law)," Eur. J. Phys. 28, L17-L25 (2007).
92. G. Troll and P. beim Graben, "Zipf's law is not a consequence of the central limit theorem," Phys. Rev. E 57, 1347-1355 (1998).
93. Hans Christian von Baeyer, Information: The New Language of Science, Harvard University Press (2004). This book raises many profound issues. It is not an easy read even though it is well written.
94. Charles A. Whitney, Random Processes in Physical Systems: An Introduction to Probability- Based Computer Simulations, John Wiley & Sons (1990).
95. Michael M. Woolfson, Everyday Probability and Statistics, Imperial College Press (2008). An interesting book for lay people. A discussion by Eliezer Yudkowsky of the intuitive basis of Bayesian reasoning can be found at .
96. R.K.P. Zia and B. Schmittmann, "Watching a drunkard for 10 nights: A study of distributions of variances," Am. J. Phys. 71, 859-865 (2003).
97. See Problem 3.70."Is economics the next physical science?," Phys. Today 58(9), 37-42 (2005). A related book on the importance of rare events is by Nassim Nicholas Taleb, The Black Swan: The Impact of the Highly Improbable, Random House (2007).
98. Wolfgang Christian and Anne Cox. See to download a simulation of the Galton board. Other simulations related to statistical and thermal physics are also available at this site.
99. Giulio D'Agostini, "Teaching statistics in the physics curriculum: Unifying and clarifying role of subjective probability," Am. J. Phys. 67, 1260-1268 (1999). The author, whose main research interest is in particle physics, discusses subjective probability and Bayes' theorem. Section 3.4 is based in part on this article.
100. F. N. David, Games, Gods and Gambling: A History of Probability and Statistical Ideas, Dover Publications (1998).
101. Marta C. González, César A. Hidalgo, and Albert-László Barabási, "Understanding individual human mobility patterns," Nature 453, 779-782 (2008). The authors studied the trajectories of 100,000 cell phone users over a six-month period and found that human trajectories cannot be simply modeled by a Lévy flight or as an ordinary random walk. Similar studies have been done on animal trajectories. The website has many examples of the application of probability to diverse systems of interest in statistical physics.
102. T.P. Hill, "The first digit phenomenon," Am. Sci. 86, 358-363 (1998).
103. James R. Huddle, "A note on Benford's law," Math. Comput. Educ. 31, 66 (1997).
104. Gene F. Mazenko, Equilibrium Statistical Mechanics, John Wiley &Sons (2000). Sections 1.7 and 1.8 of this graduate level text discuss the functional form of the missing information.
105. Leonard Mlodinow, The Drunkard'sWalk: How Randomness Rules Our Lives, Vintage Press (2009). A popular book on how the mathematical laws of randomness affect our lives.
106. Elliott W. Montroll and Wade W. Badger, Introduction to Quantitative Aspects of Social Phenomena, Gordon and Breach (1974). The applications of probability that are discussed include traffic flow, income distributions, floods, and the stock market.
107. Elliott W. Montroll and Michael F. Shlesinger, "On the wonderful world of random walks," in Studies in Statistical Mechanics, Vol. XI of Nonequilibrium Phenomena II, edited by J. L. Lebowitz and E. W. Montroll, North-Holland (1984). An excellent article on the history of random walks.
108. Joáo Gama Oliveira and Albert-László Barabási, "Darwin and Einstein correspondence patterns," Nature 437, 1251 (2005).
109. Richard Perline, "Zipf's law, the central limit theorem, and the random division of the unit interval," Phys. Rev. E 54, 220-223 (1996).
110. The outcome of tossing a coin is not really random. See Ivars Peterson, "Heads or tails?," Science News Online, and Erica
111. Klarreich, "Toss out the toss-up: Bias in heads-or-tails," Science News 165(9), 131 (2004), . Some of the original publications include Joseph Ford, "How random is a coin toss?," Phys. Today 36(4), 40-47 (1983);
112. Some of the original publications include Joseph Ford, "How random is a coin toss?," Phys. Today 36(4), 40-47 (1983);
113. Joseph B. Keller, "The probability of heads," Am. Math. Monthly 93, 191-197 (1986)
114. Vladimir Z. Vulovic and Richard E. Prange, "Randomness of a true coin toss," Phys. Rev. A 33, 576-582 (1986).
115. S. Redner, "Random multiplicative processes: An elementary tutorial," Am. J. Phys. 58, 267- 273 (1990).
116. Jason Rosenhouse, The Monty Hall Problem: The Remarkable Story of Math's Most Contentious Brain Teaser, Oxford University Press (2009).
117. Charles Ruhla, The Physics of Chance, Oxford University Press (1992).
118. B. Schmittmann and R. K. P. Zia, "'Weather' records: Musings on cold days after a long hot Indian summer," Am. J. Phys. 67, 1269-1276 (1999). A relatively simple introduction to the statistics of extreme values. Suppose that somebody breaks the record for the 100m dash. How long do such records typically survive before they are broken?
119. Kyle Siegrist at the University of Alabama in Huntsville has developed many applets to illustrate concepts in probability and statistics. See and follow the link to Bernoulli processes.
120. J. Torres, S. Fernández, A. Gamero, and A Sola, "How do numbers begin? (The first digit law)," Eur. J. Phys. 28, L17-L25 (2007).
121. G. Troll and P. beim Graben, "Zipf's law is not a consequence of the central limit theorem," Phys. Rev. E 57, 1347-1355 (1998).
122. Hans Christian von Baeyer, Information: The New Language of Science, Harvard University Press (2004). This book raises many profound issues. It is not an easy read even though it is well written.
123. Charles A. Whitney, Random Processes in Physical Systems: An Introduction to Probability- Based Computer Simulations, John Wiley & Sons (1990).
124. Michael M. Woolfson, Everyday Probability and Statistics, Imperial College Press (2008). An interesting book for lay people. A discussion by Eliezer Yudkowsky of the intuitive basis of Bayesian reasoning can be found at .
125. R.K.P. Zia and B. Schmittmann, "Watching a drunkard for 10 nights: A study of distributions of variances," Am. J. Phys. 71, 859-865 (2003). See Problem 3.70.
126. Joan Adler, "A walk in phase space: Solidification into crystalline and amorphous states," Am. J. Phys. 67, 1145~-1148 (1999). Adler and Laird discuss the demonstration in Problem 4.56.
127. Ralph Baierlein, Thermal Physics, Cambridge University Press (1999).
128. George B. Benedek and Felix M. H. Villars, Physics with Illustrative Examples from Medicine and Biology: Statistical Physics, 2nd ed., Springer (2000).
129. Carlo Cercignani, Ludwig Boltzmann: The Man Who Trusted Atoms, Oxford University Press (1998).
130. Ruth Chabay and Bruce Sherwood, Matter & Interactions, Vol. 1, 3rd ed., John Wiley & Sons (2010). This introductory text discusses the Einstein solid in the same spirit as our text.
131. Harvey Leff and Andrew F. Rex, eds. Maxwell's Demon 2: Entropy, Classical and Quantum Information, Computing, CRC Press (2003).
132. Brian B. Laird, "Entropy, disorder and freezing," J. Chem. Educ. 76, 1388-1390 (1999). Thomas A. Moore and Daniel V. Schroeder, "A different approach to introducing statistical mechanics," Am. J. Phys. 65, 26-36 (1997).
133. Thomas A. Moore and Daniel V. Schroeder, "A different approach to introducing statistical mechanics," Am. J. Phys. 65, 26-36 (1997).
134. F. Reif, Statistical Physics, Vol. 5 of the Berkeley Physics Series, McGraw-Hill (1965).
135. W.G.V. Rosser, An Introduction to Statistical Physics, Ellis Horwood (1982). As far as we know, this book was the first to introduce the Einstein solid in the context of the counting of states and the thermal interaction of simple systems.
136. Daniel V. Schroeder, An Introduction to Thermal Physics, Addison-Wesley (1999).
137. Jan Tobochnik and Harvey Gould, "Teaching statistical physics by thinking about models and algorithms," Am. J. Phys. 76, 353-359 (2008). This article describes why Monte Carlo simulations give the correct thermodynamic averages and discusses ways of simulating systems more efficiently.
138. Jan Tobochnik, Harvey Gould, and Jon Machta, "Understanding the temperature and the chemical potential using computer simulations," Am. J. Phys. 73(8), 708-716 (2005). This article describes the demon algorithm in detail for use as an ideal thermometer and as an ideal chemical potential meter (see Section 7.2).
139. Stephen G. Brush, "History of the Lenz-Ising model," Rev. Mod. Phys. 39, 883-893 (1967).
140. Cyril Domb, The Critical Point, Taylor & Francis (2996). This graduate level monograph discusses the history of our understanding of phase transitions. Much of the history is accessible to undergraduates.
141. David L. Goodstein, States of Matter, Dover Publications (1985). This book discusses how to apply thermodynamics and statistical mechanics to gases, liquids, and solids, and reviews magnetism in solids.
142. S. Kobe, "Ernst Ising 1900-1998," Braz. J. Phys. 30(4), 649-654 (2000). Available online from several web sites.
143. D. P. Landau, Shan-Ho Tsai, and M. Exler, "A new approach to Monte Carlo simulations in statistical physics: Wang-Landau sampling," Am. J. Phys. 72, 1294-1302 (2004).
144. B. Liu and M. Gitterman, "The critical temperature of two-dimensional and threedimensional Ising models," Am. J. Phys. 71, 806-808 (2003). The authors give a simple argument for the value of the critical temperature of the Ising model which gives the exact result in two dimensions and an approximate result in three dimensions [see Problem 5.36(c)].
145. F. Mandl, Statistical Physics, 2nd ed., John Wiley & Sons (1988). This text has a good discussion of the thermodynamics of magnetism.
146. Daniel C. Mattis, The Theory of Magnetism Made Simple, World Scientific (2006). The Bohr- van Leeuwen theorem is discussed in Section 1.6.
147. M. E. J. Newman and G. T. Barkema, Monte Carlo Methods in Statistical Physics, Clarendon Press (1999).
148. Peter Palffy-Muhoraya, "The single particle potential in mean-field theory," Am. J. Phys. 70, 433-437 (2002).
149. H. Eugene Stanley, Introduction to Phase Transitions and Critical Phenomena, Oxford University Press (1971). The discussion of the high temperature expansion in Section 5.10.3 is based in part on this book.
150. D. Stauffer, "Social applications of two-dimensional Ising models," Am. J. Phys. 76, 470-473 (2008).
151. Jan Tobochnik and Harvey Gould, "Teaching statistical physics by thinking about models and algorithms," Am. J. Phys. 76, 353-359 (2008).
152. More information about Bose-Einstein condensation can be found at , , and .
153. Vanderlei Bagnato and Daniel Kleppner, "Bose-Einstein condensation in low-dimensional traps," Phys. Rev. A 44, 7439-7441 (1991).
154. Ralph Baierlein, "The elusive chemical potential," Am. J. Phys. 69, 428-434 (2001).
155. Roger Balian and Jean-Paul Blaizot, "Stars and statistical physics: A teaching experience," Am. J. Phys. 67, 1189-1206 (1999). The article, which is part of a theme issue on thermal and statistical mechanics, contains an excellent introduction to the use of statistical physics to understand stars.
156. John J. Brehm and William J. Mullin, Introduction to the Structure of Matter, John Wiley & Sons (1989); Robert Eisberg and Robert Resnick, Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles, 2nd ed., John Wiley & Sons (1985). See these books, for example, for more complete discussions of blackbody radiation.
157. Ian Duck and E. C. G. Sudarshan, Pauli and the Spin-Statistics Theorem, World Scientific (1998). This graduate-level text simplifies and clarifies the formal statements of the spinstatistics theorem, and corrects the flawed intuitive explanations that are frequently given.
158. David L. Goodstein, States of Matter, Prentice Hall (1975). An excellent text whose emphasis is on the applications of statistical mechanics to gases, liquids and solids. Chapter 3 on solids is particularly relevant to this chapter.
159. J. D. Gunton and M. J. Buckingham, "Condensation of the ideal Bose gas as a cooperative transition," Phys. Rev. 166, 152-158 (1968).
160. F. Herrmann and P. Würfel, "Light with nonzero chemical potential," Am. J. Phys. 73, 717- 721 (2005). The authors discuss thermodynamic states and processes involving light in which the chemical potential of light is nonzero.
161. Mehran Kardar, Statistical Physics of Particles, Cambridge University Press (2007). An excellent graduate level text.
162. Charles Kittel, Introduction to Solid State Physics, 7th ed. John Wiley & Sons (1996). See Chapters 5 and 6 for a discussion of the Debye model and the free electron gas.
163. W. J. Mullin and G. Blaylock, "Quantum statistics: Is there an effective fermion repulsion or boson attraction?," Am. J. Phys. 71, 1223-1231 (2003).
164. A. Pais, "Einstein and the quantum theory," Rev. Mod. Phys. 51, 863-914 (1979). This review article has a fascinating account of how Planck arrived at his famous blackbody radiation formula.
165. Donald Rogers, Einstein's Other Theory: The Planck-Bose-Einstein Theory of Heat Capacity, Princeton University Press (2005).
166. Robert H. Swendsen, "Statistical mechanics of colloids and Boltzmann's definition of the entropy," Am. J. Phys. 74, 187-190 (2006). The author argues that the usual definition of the entropy for a classical system of particles in terms of the logarithm of a volume in phase space is not fundamental and not the definition orginally given by Boltzmann. Swendsen's treatment resolves the Gibbs paradox in a novel way.
167. Robert Weinstock, "Heat capacity of an ideal free electron gas: A rigorous derivation," Am. J. Phys. 37, 1273-1279 (1969).
168. Ralph Baierlein, "The elusive chemical potential," Am. J. Phys. 69, 423-434 (2001).
169. Ralph Baierlein, Thermal Physics, Cambridge University Press (1999).
170. Craig F. Bohren and Bruce A. Albrecht, Atmospheric Thermodynamics, Oxford University Press (1998). Chapter 5 of this delightful text has an excellent discussion of water and its transformations.
171. S. C. Colbeck, "Pressure melting and ice skating," Am. J. Phys. 63, 888-890 (1995)
172. S. C. Colbeck, L. Najarian and H. B. Smith, "Sliding temperatures of ice skates," Am. J. Phys. 65, 488-492 (1997).
173. Daan Frenkel and Berend Smit, Understanding Molecular Simulation, Academic Press, San Diego (1996). This monograph discusses the Widom insertion method and many other useful algorithms.
174. L. Glasser, "Equations of state and phase diagrams," J. Chem. Educ. 79, 874-876 (2002); "Water, water, everywhere," J. Chem. Educ. 81, 414-418 (2004).
175. Mehran Kardar, Statistical Physics of Particles, Cambridge University Press (2007).
176. C. Kittel, "The way of the chemical potential," Am. J. Phys. 35, 483-487 (1967).
177. David Lind and Scott P. Sanders, The Physics of Skiing: Skiing at the Triple Point, Springer (2004). See Technote 1 for a discussion of the thermodynamics of phase changes.
178. Gene F. Mazenko, Equilibrium Statistical Mechanics, John Wiley & Sons (2000). Our Section 7.4 is based in part on Section 2.9 of this comprehensive graduate-level text.
179. Horia Metiu, Physical Chemistry: Thermodynamics, Taylor and Francis (2006). This text has a very clear and easy to follow discussion of the thermodynamics of chemical reactions, and provides many examples of how to use chemical data.
180. L. M. Quintales, J. M. Alvariño, and S. Velasco, "Computational derivation of coexistence curves for van-der-Waals-type equations," Eur. J. Phys. 9, 55-60 (1988).
181. See also John Lekner, "Parametric solution of the van der Waals liquid-vapor coexistence curve," Am. J. Phys. 50, 161-162 (1982).
182. Jan Tobochnik, Harvey Gould, and Jonathan Machta, "Understanding temperature and chemical potential using computer simulations," Am. J. Phys. 73 (8), 708-716 (2005).
183. James D. White, "The role of surface melting in ice skating," Physics Teacher 30, 495-497 (1992).
184. B. J. Alder and T. E. Wainwright, "Phase transition in elastic disks," Phys. Rev. 127, 349- 361 (1962). See also A. C. Mitus, H. Weber, and D. Marx, "Local structure analysis of the hard-disk fluid near melting," Phys. Rev. E 55, 6855-6859 (1997).
185. See also A. C. Mitus, H. Weber, and D. Marx, "Local structure analysis of the hard-disk fluid near melting," Phys. Rev. E 55, 6855-6859 (1997)
186. John A. Barker and Douglas Henderson, "What is "liquid"? Understanding the states of matter," Rev. Mod. Phys. 48, 587-671 (1976).
187. John J. Brehm and William J. Mullin, Introduction to the Structure of Matter, John Wiley & Sons (1989).
188. R. Brout and P. Carruthers, Lectures on the Many-Electron Problem, Interscience Publishers (1963). Our discussion of cumulants and the virial expansion is based on Chapter 1 of this text.
189. D. Chandler, J. D. Weeks, and H. C. Andersen, "The van der Waals picture of liquids, solids and phase transformations," Science 220, 787-794 (1983).
190. David Chandler, Introduction to Modern Statistical Mechanics, Oxford University Press (1987).
191. N. Clisby and B. M. McCoy, "Ninth and tenth order virial coefficients for hard spheres in D dimensions," J. Stat. Phys. 122, 15-57 (2006); "New results for virial coefficients of hard spheres in D dimensions," Pramana 64, 775-783 (2005).
192. New results for virial coefficients of hard spheres in D dimensions," Pramana 64, 775-783 (2005)
193. Herbert Goldstein, Charles P. Poole, and John L. Safko, Classical Mechanics, 3rd ed., Addison-Wesley (2001).
194. Jean-Pierre Hansen and Ian R. McDonald, Theory of Simple Liquids, 3rd ed., Academic Press (2006).
195. Joseph Kestin and J. R. Dorfman, A Course in Statistical Thermodynamics, Academic Press (1971). Chapter 7 in this senior/graduate text has a good discussion of the properties of real gases.
196. Stanislav Labík, Jiří Kolafa, and Anatol Malijevský, "Virial coefficients of hard spheres and hard disks up to the ninth," Phys. Rev. E 71, 021105-1-8 (2005).
197. Mariano López de Haro, Andrés Santos, and Santos Bravo Yuste, "A student-oriented derivation of a reliable equation of state for a hard-disc fluid," Eur. J. Phys. 19, 281-286 (1998).
198. Richard D. Mattuck, A Guide to Feynman Diagrams in the Many-Body Problem, 2nd ed., Dover Books (1992). Feynman diagrams are the generalization of Mayer diagrams in the context of quantum field theory.
199. K. Younge, C. Christenson, A. Bohara, J. Crnkovic, and P. Saulniera, "A model system for examining the radial distribution function," Am. J. Phys. 72, 1247-1250 (2004). An experiment suitable for undergraduates that illustrates the meaning of the radial distribution function for a system of hard disks is discussed.
200. Alastair Bruce and David Wallace, "Critical point phenoma: Universal physics at large length scales," in The New Physics, edited by Paul Davies. Cambridge University Press (1989).
201. David Chandler, Introduction to Modern Statistical Mechanics, Oxford University Press (1987). See Chapter 5 for a clear explanation of the renormalization group method.
202. R. J. Creswick, H. A. Farach, and C. P. Poole, Jr., Introduction to Renormalization Group Methods in Physics, John Wiley & Sons (1992).
203. Cyril Domb, The Critical Point: A Historical Introduction to the Modern Theory of Critical Phenomena, Taylor & Francis (1996). The physics is explained at the graduate level, but much of it is accessible to undergraduates, especially the discussion of the history of various developments.
204. H. Gould, J. Tobochnik, and W. Christian, An Introduction to Computer Simulation Methods, 3rd ed., Addison-Wesley (2006), Chap. 12.
205. Kerson Huang, Statistical Mechanics, 2nd ed., John Wiley & Sons (1987).
206. Leo P. Kadanoff, Statistical Physics: Statics, Dynamics, and Renormalization, World- Scientific (2000).
207. H. J. Maris and L. P. Kadanoff, "Teaching the renormalization group," Am. J. Phys. 46, 652-657 (1978).
208. Ramit Mehr, Tal Grossman, N. Kristianpoller, and Yuval Gefen, "Simple percolation experiment in two dimensions," Am. J. Phys. 54, 271-273 (1986).
209. Michael Plischke and Birger Bergersen, Equilibrium Statistical Physics, 3rd ed., World Scientific (2006). An excellent graduate-level text.
210. P. J. Reynolds, H. E. Stanley, and W. Klein, "A large cell Monte Carlo renormalization group for percolation," Phys. Rev. B 21, 1223-1245 (1980). Our discussion of percolation in Section 9.4 is mostly based on this paper.
211. D. Stauffer, "Percolation clusters as teaching aid for Monte Carlo simulation and critical exponents," Am. J. Phys. 45, 1001-1002 (1977).
212. Dietrich Stauffer and Amnon Aharony, Introduction to Percolation Theory, 2nd ed., Taylor & Francis (1992).
213. D. J. Wallace and R. K. P. Zia, "The renormalisation group approach to scaling in physics," Rep. Prog. Phys. 41, 1-85 (1978).
214. K. G. Wilson, "Problems in physics with many scales of length," Sci. Am. 241(8), 140-157 (1979).
215. Richard Zallen, The Physics of Amorphous Solids, John Wiley & Sons (1983). This monograph discusses applications of percolation theory.