Violation of finite-size scaling in three dimensions

European Physical Journal B

Volumn 10, Issue 4, 1999, Pages 687-703

  Chen, X S ^a,b   Dohm, V ^a  

^a RWTH AACHEN UNIVERSITY   (Germany)

^b CENTRAL CHINA NORMAL UNIVERSITY   (China)

Author keywords

05.70.Jk critical point phenomena; 64.60. i general studies of phase transitions

Indexed keywords

EID: 0000306149     PISSN: 14346028     EISSN: None     Source Type: Journal    
DOI: 10.1007/s100510050901     Document Type: Article

References (130)

1. K.G. Wilson, Phys. Rev. B 4, 3174 (1971); B 4, 3184 (1971); Rev. Mod. Phys. 55, 583 (1983).
2. K.G. Wilson, Phys. Rev. B 4, 3174 (1971); B 4, 3184 (1971); Rev. Mod. Phys. 55, 583 (1983).
3. K.G. Wilson, Phys. Rev. B 4, 3174 (1971); B 4, 3184 (1971); Rev. Mod. Phys. 55, 583 (1983).
4. M.E. Fisher, Rev. Mod. Phys. 46, 597 (1974); 70, 653 (1998).
5. M.E. Fisher, Rev. Mod. Phys. 46, 597 (1974); 70, 653 (1998).
6. J. Zinn-Justin, Quantum Field Theory and Critical Phenomena (Clarendon Press, Oxford, 1996).
7. E. Brézin, J. Phys. France 43, 15 (1982).
8. M.E. Fisher, in Critical Phenomena, Proceedings of the 1970 International School of Physics "Enrico Fermi", Course 51, edited by M.S. Green (Academic, New York, 1971).
9. M.N. Barber, in Phase Transitions and Critical Phenomena, edited by C. Domb, J.L. Lebowitz (Academic Press, New York, 1983), Vol. 8, p. 145.
10. Finite Size Scaling and Numerical Simulation of Statistical Systems, edited by V. Privman (World Scientific, Singapore, 1990).
11. V. Privman, P. C. Hohenberg, A. Aharony, in Phase Transitions and Critical Phenomena, edited by C. Domb, J.L. Lebowitz (Academic Press, New York, 1991), Vol. 14, p. 1.
12. K. Binder, Annu. Rev. Phys. Chem. 43, 33 (1992); Rep. Prog. Phys. 60, 487 (1997).
13. K. Binder, Annu. Rev. Phys. Chem. 43, 33 (1992); Rep. Prog. Phys. 60, 487 (1997).
14. Computational Methods in Field Theory, edited by H. Gausterer, C.B. Lang (Springer, Berlin, 1992).
15. V. Dohm, Phys. Scr. T 49, 46 (1993).
16. H. Meyer-Ortmanns, Rev. Mod. Phys. 68, 473 (1996).
17. D. Amit, Field Theory, the Renormalization Group and Critical Phenomena (World Scientific, Singapore, 1984).
18. J.M. Luck, Phys. Rev. B 31, 3069 (1985).
19. D. Schmeltzer, Phys. Rev. B 32, 7512 (1985).
20. E. Brézin, J. Zinn-Justin, Nucl. Phys. B 257 [FS14], 867 (1985).
21. J. Rudnick, H. Guo, D. Jasnow, J. Stat. Phys. 41, 353 (1985).
22. E. Eisenriegler, Z. Phys. B 61, 299 (1985).
23. H.W. Diehl, in Phase Transition and Critical Phenomena, edited by C. Domb, J.L. Lebowitz (Academic, London, 1986), Vol. 10, p. 76.
24. Y.Y. Goldschmidt, Nucl. Phys. B 280, 340 (1987); 285, 519 (1987).
25. Y.Y. Goldschmidt, Nucl. Phys. B 280, 340 (1987); 285, 519 (1987).
26. J.C. Niel, J. Zinn-Justin, Nucl. Phys. B 280, 355 (1987).
27. H.W. Diehl, Z. Phys. B 66, 211 (1987).
28. E. Eisenriegler, R. Tomaschitz, Phys. Rev. B 35, 4876 (1987).
29. W. Huhn, V. Dohm, Phys. Rev. Lett. 61, 1368 (1988).
30. H. Guo, D. Jasnow, Phys. Rev. B 35, 1846 (1987); B 39, 753 (1989)(E).
31. H. Guo, D. Jasnow, Phys. Rev. B 35, 1846 (1987); B 39, 753 (1989)(E).
32. H.K. Janssen, B. Schaub, B. Schmittmann, Z. Phys. B 71, 377 (1988); J. Phys. A 21, L427 (1988).
33. H.K. Janssen, B. Schaub, B. Schmittmann, Z. Phys. B 71, 377 (1988); J. Phys. A 21, L427 (1988).
34. J.C. Niel, Phys. Rev. B 37, 2156 (1988).
35. V. Dohm, Z. Phys. B 75, 109 (1989).
36. D. Frank, V. Dohm, Phys. Rev. Lett. 62, 1864 (1989); Z. Phys. B 84, 442 (1991).
37. D. Frank, V. Dohm, Phys. Rev. Lett. 62, 1864 (1989); Z. Phys. B 84, 442 (1991).
38. P. Hasenfratz, H. Leutwyler, Nucl. Phys. B 343, 241 (1990); M. Göckeler, H. Leutwyler, Nucl. Phys. B 350, 228 (1991).
39. P. Hasenfratz, H. Leutwyler, Nucl. Phys. B 343, 241 (1990); M. Göckeler, H. Leutwyler, Nucl. Phys. B 350, 228 (1991).
40. R. Schmolke, A. Wacker, V. Dohm, D. Frank, Physica B 165&166, 575 (1990).
41. M. Krech, S. Dietrich, Phys. Rev. Lett. 66, 345 (1991); Phys. Rev. A 46, 1886 (1992); A 46, 1922 (1992).
42. M. Krech, S. Dietrich, Phys. Rev. Lett. 66, 345 (1991); Phys. Rev. A 46, 1886 (1992); A 46, 1922 (1992).
43. M. Krech, S. Dietrich, Phys. Rev. Lett. 66, 345 (1991); Phys. Rev. A 46, 1886 (1992); A 46, 1922 (1992).
44. D. O'Connor, C.R. Stephens, Nucl. Phys. B 360, 297 (1991); J. Phys. A 25, 101 (1992); Phys. Rev. Lett. 72, 506 (1994); Int. J. Mod. Phys. A 9, 1805 (1994); Phys. Rev. E 54, 196 (1996).
45. D. O'Connor, C.R. Stephens, Nucl. Phys. B 360, 297 (1991); J. Phys. A 25, 101 (1992); Phys. Rev. Lett. 72, 506 (1994); Int. J. Mod. Phys. A 9, 1805 (1994); Phys. Rev. E 54, 196 (1996).
46. D. O'Connor, C.R. Stephens, Nucl. Phys. B 360, 297 (1991); J. Phys. A 25, 101 (1992); Phys. Rev. Lett. 72, 506 (1994); Int. J. Mod. Phys. A 9, 1805 (1994); Phys. Rev. E 54, 196 (1996).
47. D. O'Connor, C.R. Stephens, Nucl. Phys. B 360, 297 (1991); J. Phys. A 25, 101 (1992); Phys. Rev. Lett. 72, 506 (1994); Int. J. Mod. Phys. A 9, 1805 (1994); Phys. Rev. E 54, 196 (1996).
48. D. O'Connor, C.R. Stephens, Nucl. Phys. B 360, 297 (1991); J. Phys. A 25, 101 (1992); Phys. Rev. Lett. 72, 506 (1994); Int. J. Mod. Phys. A 9, 1805 (1994); Phys. Rev. E 54, 196 (1996).
49. J.J. Morris, J. Stat. Phys. 69, 539 (1992).
50. H.W. Diehl, U. Ritschel, J. Stat. Phys. 73, 1 (1993).
51. M. Krech, The Casimir Effect in Critical Systems (World Scientific, Singapore, 1994).
52. P. Sutter, V. Dohm, Physica B 194-196, 613 (1994).
53. F. Freire, D. O'Connor, C.R. Stephens, J. Stat. Phys. 74, 219 (1994); Phys. Rev. E 53, 189 (1996).
54. F. Freire, D. O'Connor, C.R. Stephens, J. Stat. Phys. 74, 219 (1994); Phys. Rev. E 53, 189 (1996).
55. A. Esser, V. Dohm, M. Hermes, J.S. Wang, Z. Phys. B 97, 205 (1995).
56. A. Esser, V. Dohm, X.S. Chen, Physica A 222, 355 (1995).
57. X.S. Chen, V. Dohm, A. Esser, J. Phys. I France 5, 205 (1995).
58. M. Krech, E. Eisenriegler, S. Dietrich, Phys. Rev. E 52, 1345 (1995).
59. X.S. Chen, V. Dohm, A.L. Talapov, Physica A 232, 375 (1996).
60. H.K. Janssen, W. Koch, Physica A 227, 66 (1996).
61. U. Ritschel, H.W. Diehl, Nucl. Phys. B 464, 512 (1996).
62. W. Koch, V. Dohm, D. Stauffer, Phys. Rev. Lett. 77, 1789 (1996).
63. X.S. Chen, V. Dohm, N. Schultka, Phys. Rev. Lett. 77, 3641 (1996); X.S. Chen, V. Dohm, Physica A 235, 555 (1997); X.S. Chen, V. Dohm, Int. J. Mod. Phys. B 12, 1277 (1998).
64. X.S. Chen, V. Dohm, N. Schultka, Phys. Rev. Lett. 77, 3641 (1996); X.S. Chen, V. Dohm, Physica A 235, 555 (1997); X.S. Chen, V. Dohm, Int. J. Mod. Phys. B 12, 1277 (1998).
65. X.S. Chen, V. Dohm, N. Schultka, Phys. Rev. Lett. 77, 3641 (1996); X.S. Chen, V. Dohm, Physica A 235, 555 (1997); X.S. Chen, V. Dohm, Int. J. Mod. Phys. B 12, 1277 (1998).
66. J. Rudnick, W. Lay, D. Jasnow, Phys. Rev. E 58, 2902 (1998).
67. S. Bhattacharyya, J.K. Bhattacharjee, Europhys. Lett. 43, 129 (1998); J. Phys. A Lett. 31, 575 (1998); Phys. Rev. B 58, 15146 (1998).
68. S. Bhattacharyya, J.K. Bhattacharjee, Europhys. Lett. 43, 129 (1998); J. Phys. A Lett. 31, 575 (1998); Phys. Rev. B 58, 15146 (1998).
69. S. Bhattacharyya, J.K. Bhattacharjee, Europhys. Lett. 43, 129 (1998); J. Phys. A Lett. 31, 575 (1998); Phys. Rev. B 58, 15146 (1998).
70. W. Koch, V. Dohm, Phys. Rev. E 58, R 1179 (1998).
71. E. Brézin, J.C. Le Guillou, J. Zinn-Justin, in Phase Transitions and Critical Phenomena, edited by C. Domb, J.L. Lebowitz (Academic, New York, 1976), Vol. 6, p. 125.
72. X.S. Chen, V. Dohm, Eur. Phys. J. B 7, 183 (1999). On the right-hand sides of equations (11), (13) and (14) the signs of the last terms have to be reversed.
73. A.E. Ferdinand, M.E. Fisher, Phys. Rev. 185, 832 (1969).
74. M.N. Barber, M.E. Fisher, Ann. Phys. (N.Y.) 77, 1 (1973).
75. M.N. Barber, Aust. J. Phys. 26, 483 (1973); J. Phys. A 10, 1335 (1977).
76. M.N. Barber, Aust. J. Phys. 26, 483 (1973); J. Phys. A 10, 1335 (1977).
77. S. Singh, R.K. Pathria, Phys. Rev. Lett. 55, 347 (1985).
78. J. Shapiro, J. Rudnick, J. Stat. Phys. 43, 51 (1986).
79. X.S. Chen, V. Dohm (in preparation).
80. V. Privman, M.E. Fisher, J. Stat. Phys. 33, 385 (1983).
81. V. Privman, in Finite Size Scaling and Numerical Simulation of Statistical Systems, edited by V. Privman (World Scientific, Singapore, 1990), p. 1.
82. K. Binder, M. Nauenberg, V. Privman, A.P. Young, Phys. Rev. B 31, 1498 (1985).
83. K. Binder, Z. Phys. B 61, 13 (1985).
84. X.S. Chen, V. Dohm, Int. J. Mod. Phys. C 9, 1073 (1998).
85. E. Luijten, K. Binder, H.W.J. Blöte, Eur. Phys. J. B (1999).
86. H.G. Ballesteros, L.A. Fernández, V. Martín-Mayor, A. Muñoz Sudupe, G. Parisi, J.J. Ruiz-Lorenzo, Phys. Lett. B 400, 346 (1997); Nucl. Phys. B 512 [FS], 681 (1998).
87. H.G. Ballesteros, L.A. Fernández, V. Martín-Mayor, A. Muñoz Sudupe, G. Parisi, J.J. Ruiz-Lorenzo, Phys. Lett. B 400, 346 (1997); Nucl. Phys. B 512 [FS], 681 (1998).
88. X.S. Chen, V. Dohm, Eur. Phys. J. B. 5, 529 (1998).
89. X.S. Chen, V. Dohm, Physica A 251, 439 (1998).
90. X.S. Chen, V. Dohm, Int. J. Mod. Phys. C 9, 1007 (1998); cond-mat/9711298.
91. F.M. Gasparini, I. Rhee, in Prog. Low Temp. Phys. XIII, edited by D.F. Breuer (North-Holland, Amsterdam, 1992), p. 1.
92. T.P. Chen, F.M. Gasparini, Phys. Rev. Lett. 40, 331 (1978); F.M. Gasparini, T.P. Chen, B. Bhattacharyya, Phys. Rev. B 23, 5797 (1981).
93. T.P. Chen, F.M. Gasparini, Phys. Rev. Lett. 40, 331 (1978); F.M. Gasparini, T.P. Chen, B. Bhattacharyya, Phys. Rev. B 23, 5797 (1981).
94. See also A. Wacker, V. Dohm, Physica B 194-196, 611 (1994).
95. G. Ahlers, R.V. Duncan, Phys. Rev. Lett. 61, 846 (1988).
96. I. Rhee, F.M. Gasparini, D.J. Bishop, Phys. Rev. Lett. 63, 410 (1989).
97. J.A. Lipa, Q. Li, Czech. J. Phys. Suppl. S1 46, 185 (1996).
98. J.A. Nissen, T.C.P. Chui, J.A. Lipa, J. Low Temp. Phys. 92, 353 (1993); M. Coleman, J.A. Lipa, Phys. Rev. Lett. 74, 286 (1995); Czech. J. Phys. Suppl. S1 46, 183 (1996).
99. J.A. Nissen, T.C.P. Chui, J.A. Lipa, J. Low Temp. Phys. 92, 353 (1993); M. Coleman, J.A. Lipa, Phys. Rev. Lett. 74, 286 (1995); Czech. J. Phys. Suppl. S1 46, 183 (1996).
100. J.A. Nissen, T.C.P. Chui, J.A. Lipa, J. Low Temp. Phys. 92, 353 (1993); M. Coleman, J.A. Lipa, Phys. Rev. Lett. 74, 286 (1995); Czech. J. Phys. Suppl. S1 46, 183 (1996).
101. J.A. Lipa, D.R. Swanson, J.A. Nissen, P.R. Williamson, Z.K. Geng, D.A. Stricker, T.C.P. Chui, U.E. Israelsson, M. Larson, J. Low Temp. Phys. 113, 849 (1998).
102. S. Mehta, M.O. Kimball, F.M. Gasparini, J. Low Temp. Phys. 113, 435 (1998); S. Mehta, F.M. Gasparini, Phys. Rev. Lett. 78, 2596 (1997); S. Mehta, Ph.D. Thesis, State University of New York at Buffalo, 1998.
103. S. Mehta, M.O. Kimball, F.M. Gasparini, J. Low Temp. Phys. 113, 435 (1998); S. Mehta, F.M. Gasparini, Phys. Rev. Lett. 78, 2596 (1997); S. Mehta, Ph.D. Thesis, State University of New York at Buffalo, 1998.
104. S. Mehta, M.O. Kimball, F.M. Gasparini, J. Low Temp. Phys. 113, 435 (1998); S. Mehta, F.M. Gasparini, Phys. Rev. Lett. 78, 2596 (1997); S. Mehta, Ph.D. Thesis, State University of New York at Buffalo, 1998.
105. For a comparison between the data of references [76] and [77] in a finite-size scaling plot see Figure 2 of V. Dohm, in Forschung unter Weltraumbedingungen, Konferenzbericht des DLR-Bilanzsymposiums auf Norderney 1998, edited by M.H. Keller, P.R. Sahm, WPF RWTH Aachen (1999).
106. H. Fu, H. Baddar, K. Kuehn, G. Ahlers, Fizika Nizkikh Temperatur 24, 101 (1998) [Low Temp. Phys. (Ukraine) 24, 69 (1998)]; in Proceedings of the 1997 NASA/JPL Microgravity Fundamental Physics Workshop, Santa Barbara, May 7-9, 1997, NASA Document D-15677 (1998), p. 72.
107. H. Fu, H. Baddar, K. Kuehn, G. Ahlers, Fizika Nizkikh Temperatur 24, 101 (1998) [Low Temp. Phys. (Ukraine) 24, 69 (1998)]; in Proceedings of the 1997 NASA/JPL Microgravity Fundamental Physics Workshop, Santa Barbara, May 7-9, 1997, NASA Document D-15677 (1998), p. 72.
108. H. Fu, H. Baddar, K. Kuehn, G. Ahlers, Fizika Nizkikh Temperatur 24, 101 (1998) [Low Temp. Phys. (Ukraine) 24, 69 (1998)]; in Proceedings of the 1997 NASA/JPL Microgravity Fundamental Physics Workshop, Santa Barbara, May 7-9, 1997, NASA Document D-15677 (1998), p. 72.
109. R. Garcia, M.H.W. Chan, preprint (1999).
110. R. Schloms, V. Dohm, Nucl. Phys. B 328, 639 (1989).
111. F. Wegner, Phys. Rev. B 5, 4529 (1972).
112. P.M. Morse, H. Feshbach, Methods of Theoretical Physics (Mc Graw-Hill, New York, 1953).
113. H. Au-Yang, M.E. Fisher, Phys. Rev. B 11, 3469 (1975); B 21, 3956 (1980).
114. H. Au-Yang, M.E. Fisher, Phys. Rev. B 11, 3469 (1975); B 21, 3956 (1980).
115. c has been noted by M.P. Gelfand and M.E. Fisher, Physica A 166, 1 (1990), see the text following their equation (4.2.1).
116. V. Dohm, Z. Phys. B 60, 61 (1985).
117. A.A. Vladimirov, D.I. Kazakov, O.V. Tarasov, Zh. Eksp. Teor. Fiz. 77 1035 (1979) [Sov. Phys. JETP 50, 521 (1979)]; K.G. Chetyrkin, S.G. Gorishny, S.A. Larin, F.V. Tkachov, Phys. Lett. B132, 351 (1983); H. Kleinert, J. Neu, V. Schulte-Frohlinde, K.G. Chetyrkin, S.A. Larin, Phys. Lett. B 272, 39 (1991); 319, 545(E) (1993).
118. A.A. Vladimirov, D.I. Kazakov, O.V. Tarasov, Zh. Eksp. Teor. Fiz. 77 1035 (1979) [Sov. Phys. JETP 50, 521 (1979)]; K.G. Chetyrkin, S.G. Gorishny, S.A. Larin, F.V. Tkachov, Phys. Lett. B132, 351 (1983); H. Kleinert, J. Neu, V. Schulte-Frohlinde, K.G. Chetyrkin, S.A. Larin, Phys. Lett. B 272, 39 (1991); 319, 545(E) (1993).
119. A.A. Vladimirov, D.I. Kazakov, O.V. Tarasov, Zh. Eksp. Teor. Fiz. 77 1035 (1979) [Sov. Phys. JETP 50, 521 (1979)]; K.G. Chetyrkin, S.G. Gorishny, S.A. Larin, F.V. Tkachov, Phys. Lett. B132, 351 (1983); H. Kleinert, J. Neu, V. Schulte-Frohlinde, K.G. Chetyrkin, S.A. Larin, Phys. Lett. B 272, 39 (1991); 319, 545(E) (1993).
120. A.A. Vladimirov, D.I. Kazakov, O.V. Tarasov, Zh. Eksp. Teor. Fiz. 77 1035 (1979) [Sov. Phys. JETP 50, 521 (1979)]; K.G. Chetyrkin, S.G. Gorishny, S.A. Larin, F.V. Tkachov, Phys. Lett. B132, 351 (1983); H. Kleinert, J. Neu, V. Schulte-Frohlinde, K.G. Chetyrkin, S.A. Larin, Phys. Lett. B 272, 39 (1991); 319, 545(E) (1993).
121. A.A. Vladimirov, D.I. Kazakov, O.V. Tarasov, Zh. Eksp. Teor. Fiz. 77 1035 (1979) [Sov. Phys. JETP 50, 521 (1979)]; K.G. Chetyrkin, S.G. Gorishny, S.A. Larin, F.V. Tkachov, Phys. Lett. B132, 351 (1983); H. Kleinert, J. Neu, V. Schulte-Frohlinde, K.G. Chetyrkin, S.A. Larin, Phys. Lett. B 272, 39 (1991); 319, 545(E) (1993).
122. S.A. Larin, M. Mönnigmann, M. Strösser, V. Dohm, Phys. Rev. B 58, 3394 (1998).
123. G.S. Joyce, in Phase Transitions and Critical Phenomena, edited by C. Domb, M.S. Green, Vol. 5 A (Academic Press, London, 1972), p.1.
124. R.J. Baxter, Exactly Solved Models in Statistical Mechanics (Academic Press, London, 1982).
125. A.M. Kahn, G. Ahlers, Phys. Rev. Lett. 74, 944 (1995).
126. G. Ahlers, F.C. Liu, V. Dohm, NASA Proposal NRA-96-HEDS-03 (1997);
127. G. Ahlers, J. Low Temp. Phys. (1999).
128. M. Barmatz, I. Hahn, F. Zhong, J. Low Temp. Phys. 113, 891 (1998); J. Rudnick, J. Morris, M. Barmatz, V. Dohm, in Proceedings of the 1997 NASA/JPL Microgravity Fundamental Physics Workshop, Santa Barbara, May 7-9, 1997, NASA Document D-15677 (1998), p. 185.
129. M. Barmatz, I. Hahn, F. Zhong, J. Low Temp. Phys. 113, 891 (1998); J. Rudnick, J. Morris, M. Barmatz, V. Dohm, in Proceedings of the 1997 NASA/JPL Microgravity Fundamental Physics Workshop, Santa Barbara, May 7-9, 1997, NASA Document D-15677 (1998), p. 185.
130. G. Parisi, Statistical Field Theory (Addison-Wesley, Reading, MA, 1992).