Triviality problem and high-temperature expansions of higher susceptibilities for the Ising and scalar-field models in four-, five-, and six-dimensional lattices

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 85, Issue 2, 2012, Pages

  Butera, P ^a   Pernici, M ^b  

^a INFN SEZIONE DI MILANO BICOCCA   (Italy)

^b INFN SEZIONE DI MILANO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

BODY CENTERED CUBIC LATTICES; CONSTRUCTIVE APPROACH; CRITICAL AMPLITUDES; EQUATION OF STATE; EUCLIDEAN QUANTUM FIELD THEORY; HIGH-DIMENSIONAL; HIGH-TEMPERATURE EXPANSION; NUMERICAL CALCULATION; RENORMALIZATION GROUP; SCALAR FIELD MODELS; SELF-INTERACTIONS; SPATIAL DIMENSION; UNIVERSAL AMPLITUDE RATIOS;

EQUATIONS OF STATE; HIGH ENERGY PHYSICS; ISING MODEL; MAGNETIC FIELDS; NUMERICAL ANALYSIS; STATISTICAL MECHANICS;

EXPANSION;

EID: 84857598428     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.85.021105     Document Type: Article

References (121)

1. K. Wilson and J. B. Kogut, Phys. Rep. C PRPLCM 0370-1573 10.1016/0370-1573(74)90023-4 12, 75 (1974).
2. E. Brezin, J. C. Le Guillou, and J. Zinn-Justin, in Phase Transitions and Critical Phenomena, Vol. VI, edited by, C. Domb, and, M. S. Green, (Academic Press, New York, 1976).
3. J. Zinn-Justin, Quantum Field Theory and Critical Phenomena, 3rd ed. (Clarendon, Oxford, 1989, 1996).
4. A. Fernandez, J. Fröhlich, and A. Sokal, Random Walks, Critical Phenomena and Triviality in Quantum Field Theory (Springer-Verlag, Berlin, 1992).
5. K. Symanzik, Euclidean Quantum Field Theory in Local Quantum Theory, edited by, R. Jost, (Academic Press, New York, 1969).
6. D. Callaway, Phys. Rep. PRPLCM 0370-1573 10.1016/0370-1573(88)90008-7 167, 241 (1988).
7. A. Sokal, Annales de l'Institut Henry Poincaré A 37, 31 (1982);
8. A. Sokal, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(79)90633-9 71, 451 (1979).
9. L. D. Landau and I. Ya. Pomeranchuk, Dokl. Akad. Nauk USSR 102, 489 (1955);
10. I. Pomeranchuk, V. V. Sudakov, and K. A. Ter Martirosian, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.103.784 103, 784 (1956).
11. M. Aizenman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.47.1 47, 1 (1981).
12. J. Fröhlich, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(82) 90088-8 200, 281 (1982).
13. C. A. de Carvalho, J. Fröhlich, and S. Caracciolo, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(83)90213-4 215, 209 (1983).
14. T. Hara, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01009035 47, 57 (1987);
15. T. Hara and H. Tasaki, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01009036 47, 99 (1987);
16. T. Hattori, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.525932 24, 2200 (1983).
17. S. B. Shlosman, Sov. Phys. Dokl. 33, 905 (1988).
18. J. P. Eckmann and R. Epstein, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01197509 64, 95 (1979).
19. D. C. Brydges, J. Fröhlich, and A. D. Sokal, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01211157 91, 141 (1983).
20. G. Gallavotti and V. Rivasseau, Ann. Inst. Henri Poincaré Physique Theorique 40, 185 (1984).
21. P. Cea, M. Consoli, and L. Cosmai, Mod. Phys. Lett. A MPLAEQ 0217-7323 10.1142/S0217732398002515 13, 2361 (1998);
22. P. Cea, M. Consoli, L. Cosmai, and P. M. Stevenson, Mod. Phys. Lett. A MPLAEQ 0217-7323 10.1142/S0217732399001760 14, 1673 (1999);
23. P. Cea. and L. Cosmai, e-print arXiv: hep-lat/0407024;
24. M. Consoli, e-print arXiv: 1101.1894.
25. I. M. Suslov, J. Exp. Theor. Phys. JTPHES 1063-7761 10.1134/1.1391515 93, 1 (2001) (Pubitemid 33319656)
26. I. M. Suslov, [Zh. Eksp. Teor. Fiz. 120, 5 (2001)]
27. I. M. Suslov, J. Exp. Theor. Phys. JTPHES 1063-7761 10.1134/ S1063776108090094 107, 413 (2008)
28. I. M. Suslov, [Zh. Eksp. Teor. Fiz. 134, 490 (2008];
29. e-print arXiv: 0804.0368;
30. I. M. Suslov, Appl. Num. Math. ANMAEL 0168-9274 10.1016/j.apnum.2010.05. 006 60, 1418 (2010);
31. I. M. Suslov, J. Exp. Theor. Phys. JTPHES 1063-7761 10.1134/ S1063776110061184 112, 274 (2011)
32. I. M. Suslov, [Zh. Eksp. Teor. Fiz. 139, 319 (2011)].
33. J. Balog, A. Duncan, R. Willey, F. Niedermayer, and P. Weisz, Nucl. Phys. B NUPBBO 0550-3213 10.1016/j.nuclphysb.2005.01.005 714, 256 (2005); (Pubitemid 40518341)
34. J. Balog, F. Niedermayer, and P. Weisz, Nucl. Phys. B NUPBBO 0550-3213 10.1016/j.nuclphysb.2006.02.026 741, 390 (2006). (Pubitemid 43566454)
35. V. Dohm, Phys. Rev. E NUPBBO 1539-3755 10.1103/PhysRevE.77.061128 77, 061128 (2008).
36. D. Stauffer, Braz. J. Phys. BJPHE6 0103-9733 10.1590/S0103- 97332000000400029 30, 787 (2000);
37. M. A. Sumour, D. Stauffer, M. M. Shabat, and A. H. El-Astal, e-print arXiv: cond-mat/0603087.
38. H. W. Blöte and E. Luijten, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i1997-00284-x 38, 565 (1997);
39. E. Luijten, K. Binder, and H. W. Blöte, Eur. Phys. J. B EPJBFY 1434-6028 10.1007/s100510050768 9, 289 (1999).
40. N. Aktekin, Physica A PHYADX 0378-4371 10.1016/S0378-4371(00)00358-7 290, 123 (2001). (Pubitemid 32092292)
41. Z. Merdan and R. Erden, Phys. Lett. A PYLAAG 0375-9601 10.1016/j.physleta.2004.08.030 330, 403 (2004).
42. J. L. Jones and A. P. Young, Phys. Rev. B PYLAAG 1098-0121 10.1103/PhysRevB.71.174438 71, 174438 (2005). (Pubitemid 43285304)
43. B. Freedman, P. Smolenski, and D. Weingarten, Phys. Lett. B PYLBAJ 0370-2693 10.1016/0370-2693(82)90790-0 113, 481 (1982).
44. I. A. Fox and I. G. Halliday, Phys. Lett. B PYLBAJ 0370-2693 10.1016/0370-2693(85)90875-5 159, 148 (1985).
45. I. T. Drummond, S. Duane, and R. R. Horgan, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(87)90137-4 280, 25 (1987).
46. W. Bernreuther, M. Göckeler, and M. Kremer, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(88)90253-2 295, 211 (1988).
47. Ch. Frick, K. Jansen, J. Jersak, I. Montvay, G. Münster, and P. Seuferling, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(90)90218-3 331, 515 (1990).
48. J. K. Kim and A. Patrascioiu, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.47.2588 47, 2588 (1993).
49. P. Grassberger, R. Hegger, and L. Schäfer, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/27/22/006 27, 7265 (1994).
50. R. Kenna and C. B. Lang, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(93)90068-Z 393, 461 (1993);
51. R. Kenna and C. B. Lang, Nucl. Phys. B NUPBBO 0550-3213 10.1016/j.nuclphysb.2004.05.012 691, 292 (2004); (Pubitemid 38808786)
52. R. Kenna and C. B. Lang, Phys. Rev. E NUPBBO 1539-3755 10.1103/PhysRevE.49.5012 49, 5012 (1994);
53. R. Kenna, Nucl. Phys. B NUPBBO 0550-3213 10.1016/j.nuclphysb.2004.05.012 691, 292 (2004). (Pubitemid 38808786)
54. E. Bittner, W. Janke, and H. Markum, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.66.024008 66, 024008 (2002).
55. P. H. Lundow and K. Markström, Phys. Rev. E PRVDAQ 1539-3755 10.1103/PhysRevE.80.031104 80, 031104 (2009);
56. P. H. Lundow and K. Markström, Nucl. Phys. B NUPBBO 0550-3213 10.1016/j.nuclphysb.2010.12.002 845, 120 (2011).
57. M. E. Fisher and D. S. Gaunt, Phys. Rev. A PHRVAO 0031-899X 10.1103/PhysRev.133.A224 133, 224 (1964).
58. D. S. Gaunt, M. F. Sykes, and S. McKenzie, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/12/6/018 12, 871 (1979).
59. G. A. Baker and J. M. Kincaid, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.42.1431 42, 1431 (1979);
60. G. A. Baker and J. M. Kincaid, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.44.434 44, 434 (E) (1980);
61. G. A. Baker and J. M. Kincaid, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01012818 24, 469 (1981).
62. M. Lüscher and P. Weisz, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(88)90602-5 300, 325 (1988);
63. M. Lüscher and P. Weisz, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(87)90177-5 290, 25 (1987);
64. M. Lüscher and P. Weisz, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(88)90228-3 295, 65 (1988);
65. M. Lüscher and P. Weisz, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(89)90637-8 318, 705 (1989).
66. A. Vladikas and C. C. Wong, Phys. Lett. B PYLBAJ 0370-2693 10.1016/0370-2693(87)91288-3 189, 154 (1987).
67. P. Butera and M. Comi, in Fluctuating Paths and Fields, edited by, W. Janke, A. Pelster, H. J. Schmidt, and, M. Bachmann, (World Scientific, Singapore, 2000).
68. D. Stauffer and J. Adler, Int. J. Mod. Phys. C IJMPEO 0129-1831 10.1142/S0129183197000230 8, 263 (1997).
69. M. Hellmund and W. Janke, Phys. Rev. B IJMPEO 1098-0121 10.1103/PhysRevB.74.144201 74, 144201 (2006). (Pubitemid 44564630)
70. N. Prokofev and B. Svistunov, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.160601 87, 160601 (2001).
71. Y. Deng, T. M. Garoni, and A. D. Sokal, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.110601 99, 110601 (2007). (Pubitemid 47429404)
72. B. Berche, C. Chatelain, C. Dahll, R. Kenna, R. Low, and J. C. Walker, J. Stat. Mech. PRLTAO 1742-5468 10.1088/1742-5468/2008/11/P11010 (2008) P11010.
73. U. Wolff, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.79.105002 79, 105002 (2009);
74. U. Wolff, Nucl. Phys. B NUPBBO 0550-3213 10.1016/j.nuclphysb.2008.09.033 810, 491 (2009);
75. P. Weisz and U. Wolff, Nucl. Phys. B NUPBBO 0550-3213 10.1016/j.nuclphysb.2011.01.006 846, 316 (2011);
76. M. Hogervorst and U. Wolff, e-print arXiv: 1109.6186;
77. P. V. Buividovich, Nucl. Phys. B 0550-3213 10.1016/j.nuclphysb.2011.08. 010 853, 688 (2011).
78. M. Wortis, in Phase Transitions and Critical Phenomena, edited by, C. Domb, and, M. S. Green, (Academic Press, New York, 1974), Vol. 3.
79. B. G. Nickel and J. J. Rehr, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01013953 61, 1 (1990).
80. P. Butera and M. Comi, Phys. Rev. B JSTPBS 1098-0121 10.1103/PhysRevB.65. 144431 65, 144431 (2002);
81. P. Butera and M. Comi, J. Stat. Phys. JSTPBS 0022-4715 10.1023/A:1019995830014 109, 311 (2002). (Pubitemid 37133758)
82. P. Butera and M. Pernici, Phys. Rev. B JSTPBS 1098-0121 10.1103/PhysRevB.83.054433 83, 054433 (2011).
83. P. Butera and M. Comi, Phys. Rev. B JSTPBS 1098-0121 10.1103/PhysRevB.56. 8212 56, 8212 (1997).
84. P. Butera and M. Comi, Phys. Rev. B JSTPBS 1098-0121 10.1103/PhysRevB.54. 15828 54, 15828 (1996);
85. P. Butera and M. Comi, Phys. Rev. B JSTPBS 1098-0121 10.1103/PhysRevB.58. 11552 58, 11552 (1998).
86. P. Butera and M. Comi, Phys. Rev. B JSTPBS 1098-0121 10.1103/PhysRevB.72. 014442 72, 014442 (2005). (Pubitemid 43291795)
87. T. de Neef and I. G. Enting, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/10/5/013 10, 801 (1977).
88. H. Arisue and T. Fujiwara, Phys. Rev. E JPHAC5 1539-3755 10.1103/PhysRevE.67.066109 67, 066109 (2003).
89. P. Butera, M. Comi, and G. Marchesini, Phys. Rev. B JPHAC5 1098-0121 10.1103/PhysRevB.33.4725 33, 4725 (1986);
90. P. Butera, R. Cabassi, M. Comi, and G. Marchesini, Comput. Phys. Commun. CPHCBZ 0010-4655 10.1016/0010-4655(87)90024-5 44, 143 (1987);
91. P. Butera, M. Comi, and G. Marchesini, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(88)90584-6 300, 1 (1988);
92. P. Butera, M. Comi, and G. Marchesini, Phys. Rev. B NUPBBO 1098-0121 10.1103/PhysRevB.40.534 40, 534 (1989).
93. P. Butera and M. Comi, Phys. Rev. B NUPBBO 1098-0121 10.1103/PhysRevB.46. 11141 46, 11141 (1992);
94. P. Butera and M. Comi, Phys. Rev. B NUPBBO 1098-0121 10.1103/PhysRevB.50. 3052 50, 3052 (1994);
95. P. Butera and M. Comi, Ann. Comb. NUPBBO 0218-0006 10.1007/BF01608788 3, 277 (1999);
96. P. Butera and M. Pernici, Physica A PHYADX 0378-4371 10.1016/j.physa. 2008.08.011 387, 6293 (2008);
97. P. Butera and M. Pernici, Phys. Rev. B PHYADX 1098-0121 10.1103/PhysRevB.78.054405 78, 054405 (2008);
98. P. Butera and M. Pernici, Phys. Rev. B PHYADX 1098-0121 10.1103/PhysRevB.80.054408 80, 054408 (2009).
99. D. L. Hunter and G. A. Baker, Phys. Rev. B PHYADX 1098-0121 10.1103/PhysRevB.7.3346 7, 3346 (1972).
100. M. E. Fisher and H. Au-Yang, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/12/10/014 12, 1677 (1979).
101. A. J. Guttmann, in Phase Transitions and Critical Phenomena, edited by, C. Domb, and, J. L. Lebowitz, (Academic Press, New York, 1989), Vol. 13, p. 1.
102. S. Katsura, N. Yazaki, and M. Takaishi, Can. J. Phys. CJPHAD 0008-4204 10.1139/p77-210 55, 1648 (1977).
103. S. McKenzie, Can. J. Phys. CJPHAD 0008-4204 10.1139/p79-173 57, 1239 (1979).
104. M. Gofman, J. Adler, A. Aharony, A. B. Harris, and D. Stauffer, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01049970 71, 1221 (1993).
105. C. M. Bender and S. Boettcher, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.51.1875 51, 1875 (1995).
106. B. Widom, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1696618 41, 3898 (1965).
107. C. Domb and D. Hunter, Proc. Phys. Soc. PPSOAU 0370-1328 10.1088/0370-1328/86/5/127 86, 1147 (1965).
108. A. Z. Patashinski and V. L. Pokrovskii, Sov. Phys. JETP 23, 292 (1966)
109. A. Z. Patashinski and V. L. Pokrovskii, [Zh. Eksp. Teor. Fiz. 50, 439 (1966)].
110. L. P. Kadanoff, Physics 2, 263 (1966).
111. M. E. Fisher, Physics 3, 255 (1967).
112. G. S. Joyce, in Phase Transitions and Critical Phenomena, edited by, C. Domb, and, M. S. Green, (Academic Press, London, 1972), Vol. 2, p. 375.
113. M. E. Fisher (private communication) reported in Ref. [73].
114. A. J. Guttmann, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/14/1/023 14, 233 (1981).
115. P. Butera and M. Comi, Phys. Rev. E JPHAC5 1539-3755 10.1103/PhysRevE.55. 6391 55, 6391 (1997).
116. R. Guida and J. Zinn-Justin, Nucl. Phys. B NUPBBO 0550-3213 10.1016/S0550-3213(96)00704-3 489, 626 (1997).
117. P. G. Watson, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/2/10/124 2, 1883 (1969).
118. J. Zinn-Justin, J. Phys. JPRAAJ 0368-3842 10.1051/jphys:01981004206078300 42, 783 (1981).
119. M. E. Fisher (private communication).
120. J. Adler and V. Privman, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/ 14/11/008 14, L463 (1981).
121. E. Brezin, J. Phys. Lett. JPSLBO 0302-072X 10.1051/jphyslet: 0197500360305100 36, L51 (1975).