Quantum phase transitions in electronic systems

Annalen der Physik (Leipzig)

Volumn 9, Issue 6, 2000, Pages 403-440

  Vojta, Thomas ^a  

^a CHEMNITZ UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ANTIFERROMAGNETISM; ELECTRON TRANSITIONS; FERROMAGNETISM; MAGNETIC MATERIALS; MAGNETIZATION; PHASE TRANSITIONS;

ITINERANT MAGNETS; METAL-INSULATOR TRANSITION; QUANTUM PHASE TRANSITION;

QUANTUM ELECTRONICS;

EID: 0033690743     PISSN: 00033804     EISSN: None     Source Type: Journal    
DOI: 10.1002/1521-3889(200006)9:6<403::AID-ANDP403>3.0.CO;2-R     Document Type: Article

References (151)

1. T. Andrews, Phil. Trans. R. Soc. 159 (1869) 575
2. J. D. van der Waals, PhD thesis, University of Leiden 1873
3. P. Curie, Ann. Chim. Phys. 5 (1895) 289
4. P. Weiss, J. Phys. Radium (Paris) 6 (1907) 667
5. L. D. Landau, Phys. Z. Sowjun. 11 (1937) 26; ibid 545; Zh. Eksp. Teor. Fiz 7 (1937) 19; ibid 627
6. L. D. Landau, Phys. Z. Sowjun. 11 (1937) 26; ibid 545; Zh. Eksp. Teor. Fiz 7 (1937) 19; ibid 627
7. L. D. Landau, Phys. Z. Sowjun. 11 (1937) 26; ibid 545; Zh. Eksp. Teor. Fiz 7 (1937) 19; ibid 627
8. L. D. Landau, Phys. Z. Sowjun. 11 (1937) 26; ibid 545; Zh. Eksp. Teor. Fiz 7 (1937) 19; ibid 627
9. E. A. Guggenheim, J. Chem. Phys. 13 (1945) 253
10. L. Onsager, Phys. Rev. 65 (1944) 117
11. B. Widom, J. Chem. Phys. 43 (1965) 3892
12. L. P. Kadanoff, Physics 2 (1966) 263
13. K. G. Wilson, Phys. Rev. B 4 (1971) 3174; ibid 3184
14. K. G. Wilson, Phys. Rev. B 4 (1971) 3174; ibid 3184
15. P. Meakin, Phys. Rep. 235 (1993) 189
16. J. Marro and R. Dickman, Non-equilibrium phase transitions in lattice models, Cambridge University Press, Cambridge 1997
17. H. van Beijeren (Editor), Proc. 9th Int. Summerschool on Fundamental Problems in Statistical Mechanics, Phys. Rep. 301 (1998) nos. 1-3
18. J. A. Hertz, Phys. Rev. B 14 (1976) 1165
19. M. Suzuki, Progr. Theor. Phys. 56 (1976) 1454
20. M. T. Beal-Monod, Solid State Commun. 14 (1974) 677
21. D. Belitz and T. R. Kirkpatrick, Rev. Mod. Phys. 66 (1994) 261
22. S. Sachdev, in Proc. 19th IUPAP Int. Conf. on Statistical Physics edited by H. Bailin, World Scientific, Singapore 1996, p.289
23. S. L. Sondhi, S. M. Girvin, J. P. Carini, and D. Shahar, Rev. Mod. Phys. 69 (1997) 315
24. T. R. Kirkpatrick and D. Belitz, in Electronic correlations in the solid state edited by N. H. March, to be published by Imperial College Press, cond-mat/9707001
25. D. Belitz and T. R. Kirkpatrick, in Models and kinetic methods for non-equilibrium many-body systems edited by J. Karkheck, Kluwer Academic, Dordrecht 1998
26. S. Sachdev and M. Vojta, Physica B 280, 333 (2000)
27. S. Sachdev, Quantum phase transitions, Cambridge University Press, Cambridge 1999
28. S.-K. Ma, Modern Theory of Critical Phenomena, Benjamin, Reading 1976
29. N. Goldenfeld, Lectures on phase transitions and the renormalization group, Addison-Wesley, Reading 1992
30. V. L. Ginzburg, Sov. Phys. - Sol. State 2 (1960) 1824
31. S. Chakravarty, B. I. Halperin, and D. R. Nelson, Phys. Rev. B 39 (1989) 2344
32. T. H. Berlin and M. Kac, Phys. Rev. 86 (1952) 821
33. H. E. Stanley, Phys. Rev. 176 (1968) 718
34. G. S. Joyce, Phys. Rev. 146 (1966) 349
35. J. M. Kosterlitz, D. J. Thouless, and R. C. Jones, Phys. Rev. Lett. 36 (1976) 1217
36. A. Jagannathan and J. Rudnick, J. Phys. A 22 (1989) 513
37. R. M. Hornreich and H. G. Schuster, Phys. Rev. B 26 (1982) 3929
38. T. Vojta, J. Phys. A 26 (1993) 2883; T. Vojta and M. Schreiber, Phys. Rev. B 50 (1994) 1272
39. T. Vojta, J. Phys. A 26 (1993) 2883; T. Vojta and M. Schreiber, Phys. Rev. B 50 (1994) 1272
40. T. Vojta and M. Schreiber, Phys. Rev. B 49 (1994) 7861
41. M. E. Fisher and M. N. Barber, Phys. Rev. Lett. 28 (1972) 1516
42. J. Rudnick, in Finite Size Scaling and Numerical Simulation of Statistical Systems, edited by V. Privman, World Scientific, Singapore 1990, p.141
43. G. S. Joyce, in Phase Transitions and Critical Phenomena vol. 2 edited by C. Domb and M. S. Green, Academic Press, New York 1972
44. A. M. Khorunzhy, B. A. Khoruzhenko, L. A. Pastur, and M. V. Shcherbina, in Phase Transitions and Critical Phenomena vol. 15 edited by C. Domb and J. Lebowitz, Academic Press, New York 1992
45. G. Obermair, in Dynamical aspects of critical phenomena edited by J. I. Budnick and M. P. Kawatra, Gordon and Breach, New York 1972
46. T. M. Nieuwenhuizen, Phys. Rev. Lett. 74 (1995) 4293
47. T. Vojta, Phys. Rev. B 53 (1996) 710
48. T. Vojta and M. Schreiber, Phys. Rev. B 53 (1996) 8211
49. L. D. Landau, Zh. Eksp. Teor. Fiz 30 (1956) 1058 [Sov. Phys. JETP 3 (1956) 920]
50. L. D. Landau, Zh. Eksp. Teor. Fiz 30 (1956) 1058 [Sov. Phys. JETP 3 (1956) 920]
51. L. D. Landau, Zh. Eksp. Teor. Fiz 32 (1957) 59 [Sov. Phys. JETP 5 (1957) 101]
52. L. D. Landau, Zh. Eksp. Teor. Fiz 32 (1957) 59 [Sov. Phys. JETP 5 (1957) 101]
53. C. Pfleiderer, G. J. McMullan, and G. G. Lonzarich, Physica B 206 & 207 (1995) 847
54. C. Pfleiderer, G. J. McMullan, S. R. Julian, and G. G. Lonzarich, Phys. Rev. B 55 (1997) 8330, and references therein
55. K. Adachi et al., J. Phys. Soc. Japan 47 (1979) 675
56. T. Sakakibara, T. Goto, K. Yoshimura, and K. Fukamichi J. Phys. Condens. Matter 2 (1990) 3381
57. A. J. Millis, Phys. Rev. B 48 (1993) 7183
58. T. Moriya, Spin fluctuations in itinerant electron magnetism, Springer, Berlin 1985
59. S. Sachdev, Z. Phys. B 94 (1994) 469
60. T. Vojta, D. Belitz, R. Narayanan, and T. R. Kirkpatrick, Europhys. Lett. 36 (1996), 191
61. T. Vojta, D. Belitz, R. Narayanan, and T. R. Kirkpatrick, Z. Phys. B 103 (1997) 451
62. J. W. Negele and H. Orland, Quantum many-particle systems, Addison-Wesley, New York 1988
63. J. Hubbard, Phys. Rev. Lett. 3 (1959) 77
64. R. L. Stratonovich, Dokl. Akad. Nauk SSSR 115 (1957) 1907 [Sov. Phys. Dokl. 2 (1957) 416]
65. R. L. Stratonovich, Dokl. Akad. Nauk SSSR 115 (1957) 1907 [Sov. Phys. Dokl. 2 (1957) 416]
66. E. C. Stoner, Proc. Roy. Soc. A 165 (1938) 372
67. D. Belitz, T. R. Kirkpatrick, and T. Vojta, Phys. Rev. B 55 (1997) 9452
68. B. Schmittmann and R. K. P. Zia, Phys. Rep. 301 (1998) 45
69. P. C. Hohenberg and B. I. Halperin, Rev. Mod. Phys. 49 (1977) 435
70. R. M. White, Quantum Theory of Magnetism, McGraw-Hill, New York 1970
71. T. Vojta, D. Belitz, T.R. Kirkpatrick, R. Narayanan, Ann. Phys. (Leipzig) 8 (1999) 593
72. D. Belitz, T. R. Kirkpatrick and T. Vojta, Phys. Rev. Lett 82 (1999) 4707
73. D. Belitz, T. R. Kirkpatrick, A. Millis, and T. Vojta, Phys. Rev. B 58 (1998) 14155
74. T. R. Kirkpatrick and D. Belitz, Phys. Rev. B 53 (1996) 14364
75. For a pedagogical discussion, see, G. Grinstein, in Fundamental Problems in Statictical Mechanics VI, edited by E. G. D. Cohen, Elsevier, New York 1985, p. 147, and references therein
76. A. B. Harris, J. Phys. C 7 (1974) 1671 (1974)
77. J. Chayes, L. Chayes, D. S. Fisher, and T. Spencer, Phys. Rev. Lett. 57 (1986) 2999
78. For a recent discussion concerning the validity of the Harris criterion, see, F. Pazamandi, R. T. Scalettar, and G. Zimanyi, Phys. Rev. Lett. 79 (1997) 5130; S. Wiseman and E. Domany, Phys. Rev. Lett. 81 (1998) 22; A. Aharony, A. B. Harris, and S. Wiseman, Phys. Rev. Lett. 81 (1998) 252
79. For a recent discussion concerning the validity of the Harris criterion, see, F. Pazamandi, R. T. Scalettar, and G. Zimanyi, Phys. Rev. Lett. 79 (1997) 5130; S. Wiseman and E. Domany, Phys. Rev. Lett. 81 (1998) 22; A. Aharony, A. B. Harris, and S. Wiseman, Phys. Rev. Lett. 81 (1998) 252
80. For a recent discussion concerning the validity of the Harris criterion, see, F. Pazamandi, R. T. Scalettar, and G. Zimanyi, Phys. Rev. Lett. 79 (1997) 5130; S. Wiseman and E. Domany, Phys. Rev. Lett. 81 (1998) 22; A. Aharony, A. B. Harris, and S. Wiseman, Phys. Rev. Lett. 81 (1998) 252
81. J. Villain, J. Phys. (Paris) 46 (1985) 1843
82. D. S. Fisher, Phys. Rev. Lett. 56 (1986) 416
83. A. E. Nash, A. R. King, and V. Jaccarino, Phys. Rev. B 43 (1991) 1272
84. B. M. McCoy and T. T. Wu, Phys. Rev. 176 (1968) 631; ibid 188 (1969) 982
85. B. M. McCoy and T. T. Wu, Phys. Rev. 176 (1968) 631; ibid 188 (1969) 982
86. B. M. McCoy, Phys. Rev. 188 (1969) 1014
87. R. Shankar and G. Murthy, Phys. Rev. B 36 (1987) 536
88. D. S. Fisher, Phys. Rev. B 51 (1995) 6411
89. R. B. Griffiths, Phys. Rev. Lett. 23 (1969) 17
90. V. Dotsenko, A. B. Harris, D. Sherrington, and R. B. Stinchcombe, J. Phys. A 28 (1995) 3093
91. M. C. de Andrade, R. Chau, R. P. Dickey, N. R. Dilley, E. J. Freeman, D. A. Gajewski, M. B. Maple, R. Movshovich, A. H. Castro Neto, and G. Castilla, Phys. Rev. Lett. 81 (1998) 5620
92. J. Kisker and A.P. Young, Phys. Rev. B 58 (1998) 14397
93. C. Pich, A. P. Young, H. Rieger, and N. Kawashima, Phys. Rev. Lett. 81 (1998) 5916
94. S. F. Edwards and P. W. Anderson, J. Phys. F 5 (1975) 965
95. R. Narayanan, T. Vojta, D. Belitz, and T. R. Kirkpatrick, Phys. Rev. Lett. 82 (1999) 5132; Phys. Rev. B 60 (1999) 10150
96. R. Narayanan, T. Vojta, D. Belitz, and T. R. Kirkpatrick, Phys. Rev. Lett. 82 (1999) 5132; Phys. Rev. B 60 (1999) 10150
97. R. Narayanan, T. Vojta, D. Belitz and T. R. Kirkpatrick, Ann. Phys. (Leipzig) 8 (1999) SI-185
98. T. R. Kirkpatrick and D. Belitz, Phys. Rev. Lett. 76 (1996) 2571; ibid 78 (1997) 1197
99. T. R. Kirkpatrick and D. Belitz, Phys. Rev. Lett. 76 (1996) 2571; ibid 78 (1997) 1197
100. R. N. Bhatt and P. A. Lee, Phys. Rev. Lett. 48 (1982) 344
101. R. N. Bhatt and D. S. Fisher, Phys. Rev. Lett. 68 (1992) 3072
102. P. W. Anderson, Phys. Rev. 109 (1958) 1492
103. B. Kramer and A. MacKinnon, Rep. Progr. Phys. 56 (1993) 1469
104. E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, Phys. Rev. Lett. 42 (1979) 637
105. B. L. Altshuler and A. G. Aronov, in Electron-electron interactions in disordered systems edited by A. L. Efros and M. Pollak, North-Holland, Amsterdam 1985
106. P. A. Lee and T. V. Ramakrishnan, Rev. Mod. Phys. 57 (1985) 287
107. A. M. Finkelstein, Zh. Eksp. Teor. Fiz. 84 (1983) 168 [Sov. Phys. JETP 57 (1983) 97]
108. A. M. Finkelstein, Zh. Eksp. Teor. Fiz. 84 (1983) 168 [Sov. Phys. JETP 57 (1983) 97]
109. S. V. Kravchenko, G. V. Kravchenko, J. E. Furneaux, V. M. Pudalov, and M. D'Iorio, Phys. Rev. B 50 (1994) 8039
110. S. V. Kravchenko, W. E. Mason, G. E. Bowker, J. E. Furneaux, V. M. Pudalov, and M. D'Iorio, Phys. Rev. B 51 (1995) 7038
111. D. Popovich, A. B. Fowler, and S. Washburn, Phys. Rev. Lett. 79 (1997) 1543
112. P.T. Coleridge, R.L. Williams, Y. Feng, and P. Zawadski, Phys. Rev. B 56 (1997) R12764; Y. Hanein, U. Meirav, D. Shahar, C. C. Li, D. C. Tsui, and H. Shtrikman, Phys. Rev. Lett 80 (1998) 1288; M. Y. Simmons, A. R. Hammilton, M. Pepper, E. H. Linfield, P. D. Rose, D. A. Richie, A. K. Savchenko, and T. G. Griffiths, Phys. Rev. Lett. 80 (1998) 1292
113. P.T. Coleridge, R.L. Williams, Y. Feng, and P. Zawadski, Phys. Rev. B 56 (1997) R12764; Y. Hanein, U. Meirav, D. Shahar, C. C. Li, D. C. Tsui, and H. Shtrikman, Phys. Rev. Lett 80 (1998) 1288; M. Y. Simmons, A. R. Hammilton, M. Pepper, E. H. Linfield, P. D. Rose, D. A. Richie, A. K. Savchenko, and T. G. Griffiths, Phys. Rev. Lett. 80 (1998) 1292
114. P.T. Coleridge, R.L. Williams, Y. Feng, and P. Zawadski, Phys. Rev. B 56 (1997) R12764; Y. Hanein, U. Meirav, D. Shahar, C. C. Li, D. C. Tsui, and H. Shtrikman, Phys. Rev. Lett 80 (1998) 1288; M. Y. Simmons, A. R. Hammilton, M. Pepper, E. H. Linfield, P. D. Rose, D. A. Richie, A. K. Savchenko, and T. G. Griffiths, Phys. Rev. Lett. 80 (1998) 1292
115. M. Y. Simmons, A. R. Hamilton, M. Pepper, E. H. Linfield, P. D. Rose, and D. A. Ritchie, cond-mat/9910368
116. C. Castellani, C. DiCastro and P. A. Lee, Phys. Rev. B 57 (1998) R9381
117. Q. Si and C. M. Varma, Phys. Rev. Lett. 81 (1998) 4951
118. S. Chakravarty, L. Yin, and E. Abrahams, Phys. Rev. B 58 (1998) R559
119. S. Chakravarty, S. Kivelson, C. Nayak, and K. Völker, Phil. Mag. B 79 (1999) 859
120. D. Belitz and T. R. Kirkpatrick, Phys. Rev. B 58 (1998) 8214; P. Phillips, Y. Wan, I Martin, S. Knych, and D. Dalidovich, Nature 395 (1998) 253; F. C. Zhang and T. M. Rice, cond-mat/ 9708050
121. D. Belitz and T. R. Kirkpatrick, Phys. Rev. B 58 (1998) 8214; P. Phillips, Y. Wan, I Martin, S. Knych, and D. Dalidovich, Nature 395 (1998) 253; F. C. Zhang and T. M. Rice, cond-mat/ 9708050
122. B. L. Altshuler and D. L. Maslov, Phys. Rev. Lett. 82 (1999) 145
123. T. M. Klapwijk and S. Das Sarma, Solid State Commun. 110 (1999) 581
124. M. A. Paalanen, S. Sachdev, R. N. Bhatt, and A. E. Ruckenstein, Phys. Rev. Lett. 57 (1986) 2061; M. A. Paalanen, J. E. Graebner, R. N. Bhatt, and S. Sachdev, Phys. Rev. Lett. 61 (1988) 597
125. M. A. Paalanen, S. Sachdev, R. N. Bhatt, and A. E. Ruckenstein, Phys. Rev. Lett. 57 (1986) 2061; M. A. Paalanen, J. E. Graebner, R. N. Bhatt, and S. Sachdev, Phys. Rev. Lett. 61 (1988) 597
126. M. Milovanovic, S. Sachdev, and R.N. Bhatt, Phys. Rev. Lett. 63 (1989) 82, and references therein
127. D. Belitz, T. R. Kirkpatrick, and T. Vojta, Phys. Rev. Lett, in press
128. A. L. Efros and F. G. Pikus, Solid State Commun. 96 (1995) 183
129. J. Talamantes, M. Pollak, and L. Elam, Europhys. Lett. 35 (1996) 511
130. F. Epperlein, M. Schreiber, and T. Vojta, Phys. Rev. B 56 (1997) 5890
131. M. Pollak, Discuss. Faraday Soc. 50 (1970) 13
132. A. L. Efros and B. I. Shklovskii, J. Phys. C 8 (1975) L49
133. A. L. Efros and B. I. Shklovskii, in Electron-electron interactions in disordered systems, edited by A. L. Efros and M. Pollak, North-Holland, Amsterdam 1985, p. 409
134. B. L. Altshuler and A. G. Aronov, Sol. State Commun. 30 1979 115
135. B. I. Shklovskii, B. Shapiro, B. R. Sears, P. Lambrianides, and H. B. Shore, Phys. Rev. B 47 (1993) 11487
136. E. Hofstetter and M. Schreiber, Phys. Rev. B 48 (1993) 16979
137. T. Vojta, F. Epperlein, and M. Schreiber, phys. stat. sol. (b) 205 (1998) 53
138. F. Epperlein, M. Schreiber, and T. Vojta, phys. stat. sol. (b) 205 (1998) 233
139. K. Kubo, J. Phys. Soc. Jpn. 12 (1957) 576
140. D. A. Greenwood, Proc. Phys. Soc., London 71 (1958) 585
141. T. Vojta, F. Epperlein, and M. Schreiber, Computer Phys. Commun. 121-122 (1999) 489
142. P. Fulde, Electron correlations in molecules and solids, Springer, Berlin 1995
143. T. Vojta, F. Epperlein, and M. Schreiber, Phys. Rev. Lett. 81 (1998) 4212
144. T. Vojta and F. Epperlein, Ann. Phys. (Leipzig) 7 (1998) 493
145. M. Schreiber, F. Epperlein, and T. Vojta, Physica A 266 (1999) 443
146. P. Schmitteckert, R. A. Jalabert, D. Weinmann, and J. L. Pichard, Phys. Rev. Lett. 81 (1998) 2308
147. G. Benenti, X. Waintal, and J. L. Pichard, Phys. Rev. Lett. 83 (1999) 1826
148. P. J. H. Denteneer, R. T. Scalettar, and N. Trivedi, cond-mat/9907246
149. W Apel and T. M. Rice, Phys. Rev. B 26 (1982) 7063
150. D. Simonian, S. V. Kravchenko, and M. P. Sarachik, ibid. 79 (1997) 2304
151. V. M. Pudalov, G. Brunthaler, A. Prinz, and G. Bauer, JETP Lett. 65 (1997) 932