Component Ginzburg-Landau Hamiltonian with cubic anisotropy: A six-loop study

Physical Review B - Condensed Matter and Materials Physics

Volumn 61, Issue 22, 2000, Pages 15136-15151

  Manuel Carmona, José ^a   Pelissetto, Andrea ^b  

^a INFN SEZIONE DI PISA   (Italy)

^b INFN SEZIONE DI ROMA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000952996     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.61.15136     Document Type: Article

References (82)

1. A. Aharony, Phys. Rev. B 8, 3349 (1973).
2. A. D. Bruce, J. Phys. C 7, 2089 (1974).
3. T. Nattermann and S. Trimper, J. Phys. A 8, 2000 (1975).
4. T. Nattermann, J. Phys. A 9, 3337 (1976).
5. A. Aharony, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. Lebowitz (Academic Press, New York, 1976), Vol. 6, p. 357.
6. A. Aharony, Phys. Rev. B 8, 4270 (1973).
7. J. Sak, Phys. Rev. B 10, 3957 (1974).
8. M. Campostrini, A. Pelissetto, P. Rossi, and E. Vicari, Phys. Rev. E 60, 3526 (1999).
9. D. J. Wallace, J. Phys. C 6, 1390 (1973).
10. A. Aharony, J. Phys. A 10, 389 (1977).
11. J. Sznajd and M. Dudziński, Phys. Rev. B 59, 4176 (1999).
12. V. J. Emery, Phys. Rev. B 11, 239 (1975).
13. M. E. Fisher, Phys. Rev. 176, 257 (1968).
14. A. Aharony, Phys. Rev. Lett. 31, 1494 (1973).
15. I. J. Ketley and D. J. Wallace, J. Phys. A 6, 1667 (1973).
16. A. D. Bruce and A. Aharony, Phys. Rev. B 11, 478 (1975).
17. E. Brézin, J. C. Le Guillou, and J. Zinn-Justin, in Phase Transitions and Critical Phenomena (Ref. 5), p. 125.
18. A. L. Korzhenevskii, Zh. Éksp. Teor. Fiz. 71, 1434 (1976) [Sov. Phys. JETP 44, 751 (1976)].
19. J. V. José, L. P. Kadanoff, S. Kirkpatrick, and D. R. Nelson, Phys. Rev. B 16, 1217 (1977).
20. K. E. Newman and E. K. Riedel, Phys. Rev. B 25, 264 (1982).
21. M. K. Grover, L. P. Kadanoff, and F. J. Wegner, Phys. Rev. B 6, 311 (1972).
22. D. R. Nelson, J. M. Kosterlitz, and M. E. Fisher, Phys. Rev. Lett. 33, 813 (1974).
23. E. Brézin, J. C. Le Guillou, and J. Zinn-Justin, Phys. Rev. B 10, 893 (1974).
24. M. C. Yalabik and A. Houghton, Phys. Lett. 61A, 1 (1977).
25. E. Domany and E. K. Riedel, J. Appl. Phys. 50, 1804 (1979).
26. M. Ferer, J. P. Van Dyke, and W. J. Camp, Phys. Rev. B 23, 2367 (1981).
27. I. O. Mayer and A. I. Sokolov, Izv. Akad. Nauk SSSR, Ser. Fiz. 51, 2103 (1987).
28. N. A. Shpot, Phys. Lett. A 142, 474 (1989).
29. I. O. Mayer, A. I. Sokolov, and B. N. Shalayev, Ferroelectrics 95, 93 (1989).
30. H. Kleinert and V. Schulte-Frohlinde, Phys. Lett. B 342, 284 (1995).
31. H. Kleinert and S. Thoms, Phys. Rev. D 52, 5926 (1995).
32. H. Kleinert, S. Thoms, and V. Schulte-Frohlinde, Phys. Rev. B 56, 14 428 (1997).
33. B. N. Shalaev, S. A. Antonenko, and A. I. Sokolov, Phys. Lett. A 230, 105 (1997).
34. M. Caselle and M. Hasenbusch, J. Phys. A 31, 4603 (1998).
35. A. I. Mudrov and K. B. Varnashev, Phys. Rev. E 58, 5371 (1998).
36. K. B. Varnashev, Phys. Rev. B 61, 14 660 (2000)
37. G. Parisi, J. Stat. Phys. 23, 49 (1980).
38. J. P. Eckmann, J. Magnen, and R. Sénéor, Commun. Math. Phys. 39, 251 (1975).
39. Commun. Math. Phys.J. Magnen and R. Sénéor, 56, 237 (1977).
40. J. S. Feldman and K. Osterwalder, Ann. Phys. (N.Y.) 97, 80 (1976).
41. J. Magnen and V. Rivasseau, Commun. Math. Phys. 102, 59 (1985).
42. L. N. Lipatov, Zh. Éksp. Teor. Fiz. 72, 411 (1977) [Sov. Phys. JETP 45, 216 (1977)].
43. E. Brézin, J. C. Le Guillou, and J. Zinn-Justin, Phys. Rev. D 15, 1544 (1977).
44. Phys. Rev. DE. BrézinJ. C. Le GuillouJ. Zinn-Justin15, 1558 (1977).
45. J. C. Le Guillou and J. Zinn-Justin, Phys. Rev. Lett. 39, 95 (1977).
46. J. C. Le GuillouJ. Zinn-JustinPhys. Rev. B 21, 3976 (1980).
47. A. B. Harris and T. C. Lubensky, Phys. Rev. Lett. 33, 1540 (1974).
48. T. C. Lubensky, Phys. Rev. B 11, 3573 (1975).
49. D. E. Khmelnitskii, Zh. Éksp. Teor. Fiz. 68, 1960 (1975) [Sov. Phys. JETP 41, 981 (1976)].
50. A. J. Bray, T. McCarthy, M. A. Moore, J. D. Reger, and A. P. Young, Phys. Rev. B 36, 2212 (1987).
51. A. J. McKane, Phys. Rev. B 49, 12 003 (1994).
52. G. Alvarez, V. Martín-Mayor, and J. J. Ruiz-Lorenzo, J. Phys. A 33, 841 (2000).
53. J. Zinn-Justin, Quantum Field Theory and Critical Phenomena, 3rd ed. (Clarendon Press, Oxford, 1996).
54. B. G. Nickel, D. I. Meiron, and G. A. Baker, Jr., “Compilation of 2-pt and 4-pt graphs for continuum spin models, ” University Guelph report, 1977 (unpublished).
55. B. R. Heap, J. Math. Phys. 7, 1582 (1966).
56. G. A. Baker, Jr., B. G. Nickel, M. S. Green, and D. I. Meiron, Phys. Rev. Lett. 36, 1351 (1976).
57. G. A. Baker, Jr., B. G. Nickel, and D. I. Meiron, Phys. Rev. B 17, 1365 (1978).
58. S. A. Antonenko and A. I. Sokolov, Phys. Rev. E 51, 1894 (1995).
59. D. V. Pakhnin and A. I. Sokolov, this issue, Phys. Rev. B 61, 15 130 (2000).
60. R. Guida and J. Zinn-Justin, J. Phys. A 31, 8103 (1998).
61. D. B. Murray and B. G. Nickel, “Revised estimates for critical exponents for the continuum n-vector model in 3 dimensions, ” Guelph University report, 1991 (unpublished).
62. B. G. Nickel, in Phase Transitions, edited by M. Lévy, J. C. Le Guillou, and J. Zinn-Justin (Plenum, New York, 1982).
63. B. G. Nickel, Physica A 117, 189 (1991).
64. A. Pelissetto and E. Vicari, Nucl. Phys. B 519, 626 (1998).
65. A. PelissettoE. VicariNucl. Phys. B (Proc. Suppl.) 73, 775 (1999). The numerical estimates of (Formula presented) derived from the (Formula presented) expansion were affected by a numerical error; the correct results that are only slightly different from the older ones appear in Ref. 71.
66. A. Pelissetto and E. Vicari (unpublished).
67. J. C. Le Guillou and J. Zinn-Justin, J. Phys. (France) Lett. 46, L137 (1985).
68. M. Campostrini, A. Pelissetto, P. Rossi, and E. Vicari, Europhys. Lett. 38, 577 (1997).
69. M. CampostriniA. PelissettoP. RossiE. VicariPhys. Rev. E 57, 184 (1998).
70. M. CampostriniA. PelissettoP. RossiE. VicariNucl. Phys. B (Proc. Suppl.) 53, 690 (1997).
71. A. Pelissetto and E. Vicari, Nucl. Phys. B 522, 605 (1998).
72. Nucl. Phys. BA. PelissettoE. Vicari540, 639 (1999).
73. A. Pelissetto and E. Vicari, cond-mat/9911452, Nucl. Phys. B (to be published).
74. D. Kim, P. M. Levy, and L. F. Uffer, Phys. Rev. B 12, 989 (1975).
75. D. Kim and P. M. Levy, Phys. Rev. B 12, 5105 (1975).
76. A. Aharony, Phys. Rev. B 10, 3006 (1974).
77. C. Bervillier and M. Shpot, Phys. Rev. B 46, 955 (1992).
78. R. A. Pelcovits and D. R. Nelson, Phys. Lett. 57A, 23 (1976).
79. J. Rudnick, Phys. Rev. B 11, 3397 (1975).
80. Phys. Rev. BJ. Rudnick18, 1406 (1978).
81. P. Arnold, S. Sharpe, L. G. Yaffe, and Y. Zhang, Phys. Rev. Lett. 68, 2062 (1997).
82. N. Tetradis, Phys. Rev. B 431, 380 (1998).