On water, steam, and string theory

American Journal of Physics

Volumn 65, Issue 11, 1997, Pages 1042-1050

  Schmidhuber, Christof ^a  

^a UNIVERSITY OF BERN   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031494202     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.18738     Document Type: Article

References (24)

1. For a review of the renormalization group, see: K. G. Wilson and J. Kogut, "The renormalization group and the epsilon-expansion," Phys. Rep. C 12, 75-200 (1974).
2. The calculation of critical coefficients is discussed, e.g., by L. Kadanoff, W. Götze, D. Hamblen, R. Hecht, E. A. S. Lewis, V. V. Palciauskas, M. Rayl, and J. Swift, "Static Phenomena near Critical Points: Theory and Experiment," Rev. Mod. Phys. 39(2), 395-431 (1967).
3. A more recent discussion can be found in: J. Zinn-Justin, Quantum Field Theory and Critical Phenomena (Oxford U.P., New York, 1989), Chap. 25.
4. For previous pedagogical work on the renormalization group in the Americal Journal of Physics, see: J. M. Nunes da Silva, "Renormalized Vibrations of a Loaded Spring," Am. J. Phys. 62, 423-426 (1994); E. P. Raposo, S. M. de Oliviera, A. M. Nemirovsky, and M. D. Coutinho-Filho, "Random Walks: A Pedestrian Approach to Polymers, Critical Phenomena and Field Theory," ibid. 59, 633-645 (1991); P. Gosdzinsky and R. Tarrach, "Learning Quantum Field Theory from Elementary Quantum Mechanics," ibid. 59, 70-74 (1991); C. F. Tejero, "A Method for Evaluating Two-Spin Correlations of a One-Dimensional Ising Model," ibid. 56, 169-171 (1988); H. J. Maris and L. P. Kadanoff, "Teaching the Renormalization Group," ibid. 46, 652-657 (1978).
5. For previous pedagogical work on the renormalization group in the Americal Journal of Physics, see: J. M. Nunes da Silva, "Renormalized Vibrations of a Loaded Spring," Am. J. Phys. 62, 423-426 (1994); E. P. Raposo, S. M. de Oliviera, A. M. Nemirovsky, and M. D. Coutinho-Filho, "Random Walks: A Pedestrian Approach to Polymers, Critical Phenomena and Field Theory," ibid. 59, 633-645 (1991); P. Gosdzinsky and R. Tarrach, "Learning Quantum Field Theory from Elementary Quantum Mechanics," ibid. 59, 70-74 (1991); C. F. Tejero, "A Method for Evaluating Two-Spin Correlations of a One-Dimensional Ising Model," ibid. 56, 169-171 (1988); H. J. Maris and L. P. Kadanoff, "Teaching the Renormalization Group," ibid. 46, 652-657 (1978).
6. For previous pedagogical work on the renormalization group in the Americal Journal of Physics, see: J. M. Nunes da Silva, "Renormalized Vibrations of a Loaded Spring," Am. J. Phys. 62, 423-426 (1994); E. P. Raposo, S. M. de Oliviera, A. M. Nemirovsky, and M. D. Coutinho-Filho, "Random Walks: A Pedestrian Approach to Polymers, Critical Phenomena and Field Theory," ibid. 59, 633-645 (1991); P. Gosdzinsky and R. Tarrach, "Learning Quantum Field Theory from Elementary Quantum Mechanics," ibid. 59, 70-74 (1991); C. F. Tejero, "A Method for Evaluating Two-Spin Correlations of a One-Dimensional Ising Model," ibid. 56, 169-171 (1988); H. J. Maris and L. P. Kadanoff, "Teaching the Renormalization Group," ibid. 46, 652-657 (1978).
7. For previous pedagogical work on the renormalization group in the Americal Journal of Physics, see: J. M. Nunes da Silva, "Renormalized Vibrations of a Loaded Spring," Am. J. Phys. 62, 423-426 (1994); E. P. Raposo, S. M. de Oliviera, A. M. Nemirovsky, and M. D. Coutinho-Filho, "Random Walks: A Pedestrian Approach to Polymers, Critical Phenomena and Field Theory," ibid. 59, 633-645 (1991); P. Gosdzinsky and R. Tarrach, "Learning Quantum Field Theory from Elementary Quantum Mechanics," ibid. 59, 70-74 (1991); C. F. Tejero, "A Method for Evaluating Two-Spin Correlations of a One-Dimensional Ising Model," ibid. 56, 169-171 (1988); H. J. Maris and L. P. Kadanoff, "Teaching the Renormalization Group," ibid. 46, 652-657 (1978).
8. For previous pedagogical work on the renormalization group in the Americal Journal of Physics, see: J. M. Nunes da Silva, "Renormalized Vibrations of a Loaded Spring," Am. J. Phys. 62, 423-426 (1994); E. P. Raposo, S. M. de Oliviera, A. M. Nemirovsky, and M. D. Coutinho-Filho, "Random Walks: A Pedestrian Approach to Polymers, Critical Phenomena and Field Theory," ibid. 59, 633-645 (1991); P. Gosdzinsky and R. Tarrach, "Learning Quantum Field Theory from Elementary Quantum Mechanics," ibid. 59, 70-74 (1991); C. F. Tejero, "A Method for Evaluating Two-Spin Correlations of a One-Dimensional Ising Model," ibid. 56, 169-171 (1988); H. J. Maris and L. P. Kadanoff, "Teaching the Renormalization Group," ibid. 46, 652-657 (1978).
9. The bulk of the author's habilitation thesis consists of: (a) C. Schmidhuber, "Exactly Marginal Operators and Running Coupling Constants in 2D Gravity," Nucl. Phys. B 404, 342-358 (1993);
10. (b) "RG Flow on Random Surfaces with Handles and Closed String Field Theory," ibid. 453, 156-180 (1995); Err. ibid. 475, 710 (1995);
11. (c) "D-brane Actions," ibid. 467, 146-158 (1996);
12. (d) C. Schmidhuber and A. A. Tseytlin, "On String Cosmology and the RG Flow in Two-dimensional Field Theory," ibid. 426, 187-202 (1994).
13. 2, see: H. L. Lorentzen, Acta Chem. Scand. 7, 1335 (1953); Statistical Mechanics of Equilibrium and Nonequilibrium (North-Holland, Amsterdam, 1965), p. 262.
14. 2, see: H. L. Lorentzen, Acta Chem. Scand. 7, 1335 (1953); Statistical Mechanics of Equilibrium and Nonequilibrium (North-Holland, Amsterdam, 1965), p. 262.
15. The running of α in quantum electrodynamics is discussed in: M. Gell-Mann and F. Low, "Quantum Electrodynamics at Small Distances," Phys. Rev. 95, 1300-1312 (1954).
16. Asymptotic freedom was discovered in: D. J. Gross and F. Wilcek, "Ultraviolet behavior of non-Abelian gauge theories," Phys. Rev. Lett. 30, 1343-1346 (1973); H. D. Politzer, "Reliable Perturbative Results for Strong Interactions?," ibid. 30, 1346-1349 (1973).
17. Asymptotic freedom was discovered in: D. J. Gross and F. Wilcek, "Ultraviolet behavior of non-Abelian gauge theories," Phys. Rev. Lett. 30, 1343-1346 (1973); H. D. Politzer, "Reliable Perturbative Results for Strong Interactions?," ibid. 30, 1346-1349 (1973).
18. For an introduction to string theory, see: M. B. Green, J. H. Schwarz, and E. Witten, Superstring Theory (Cambridge U.P., New York, 1987).
19. The beta function for the metric in string theory is discussed, e.g., in: C. G. Callan, E. J. Martinec, D. Friedan, and M. J. Perry, "Strings in Background Fields," Nucl. Phys. B 262, 593-609 (1985); E. S. Fradkin und A. A. Tseytlin, "Effective Field Theory from Quantized Strings," Phys. Lett. B 158, 316-322 (1985).
20. The beta function for the metric in string theory is discussed, e.g., in: C. G. Callan, E. J. Martinec, D. Friedan, and M. J. Perry, "Strings in Background Fields," Nucl. Phys. B 262, 593-609 (1985); E. S. Fradkin und A. A. Tseytlin, "Effective Field Theory from Quantized Strings," Phys. Lett. B 158, 316-322 (1985).
21. That string theory contains gravity was found in: J. Scherk and J. H. Schwarz, "Dual Models for Non-Hadrons," Nucl. Phys. B 81, 118-144 (1974); T. Yoneya, "Connection of Dual Models to Electrodynamics and Gravidynamics," Prog. Theor. Phys. 51, 1907-1920 (1974).
22. That string theory contains gravity was found in: J. Scherk and J. H. Schwarz, "Dual Models for Non-Hadrons," Nucl. Phys. B 81, 118-144 (1974); T. Yoneya, "Connection of Dual Models to Electrodynamics and Gravidynamics," Prog. Theor. Phys. 51, 1907-1920 (1974).
23. Conformal field theory in two dimensions is discussed in: A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov, "Infinite Conformal Symmetry in Two-dimensional Quantum Field Theory," Nucl. Phys. B 241, 333-380 (1984).
24. I thank H. Bebie for letting me use his program. Another simulation program for the Ising model is available at the internet address http:// penguin.phy.bnl.gov/www/xtoys/xtoys.html.