From local to critical fluctuations in lattice models: A nonperturbative renormalization-group approach

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

Volumn 82, Issue 4, 2010, Pages

  MacHado, T ^a   Dupuis, N ^a  

^a UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

BEREZINSKII-KOSTERLITZ-THOULESS TRANSITION; CLASSICAL SPIN MODELS; CRITICAL FLUCTUATIONS; CRITICAL PROPERTIES; CRITICAL TEMPERATURES; FIELD THEORY; HEISENBERG MODELS; HYPERCUBIC LATTICES; INITIAL CONDITIONS; LATTICE MODELS; MEAN-FIELD SOLUTION; NONPERTURBATIVE; REFERENCE SYSTEMS; RENORMALIZATION GROUP; SQUARE LATTICES; X-Y MODEL;

CRYSTAL LATTICES; ELECTRON ENERGY ANALYZERS; MEAN FIELD THEORY; STATISTICAL MECHANICS;

THREE DIMENSIONAL;

EID: 78651297670     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.82.041128     Document Type: Article

References (52)

1. C. Wetterich, Phys. Lett. B 301, 90 (1993). 10.1016/0370-2693(93)90726-X
2. J. Berges, N. Tetradis, and C. Wetterich, Phys. Rep. 363, 223 (2002). 10.1016/S0370-1573(01)00098-9
3. B. Delamotte, e-print arXiv:cond-mat/0702365.
4. N. Dupuis and K. Sengupta, Eur. Phys. J. B 66, 271 (2008). 10.1140/epjb/e2008-00417-1
5. C. Wetterich, Phys. Rev. B 77, 064504 (2008). 10.1103/PhysRevB.77.064504
6. S. Floerchinger and C. Wetterich, Phys. Rev. A 77, 053603 (2008). 10.1103/PhysRevA.77.053603 (Pubitemid 351669587)
7. N. Dupuis and K. Sengupta, EPL 80, 50007 (2007). 10.1209/0295-5075/80/ 50007
8. N. Dupuis, Phys. Rev. Lett. 102, 190401 (2009). 10.1103/PhysRevLett.102. 190401
9. N. Dupuis, Phys. Rev. A 80, 043627 (2009). 10.1103/PhysRevA.80.043627
10. A. Sinner, N. Hasselmann, and P. Kopietz, Phys. Rev. Lett. 102, 120601 (2009). 10.1103/PhysRevLett.102.120601
11. A. Sinner, N. Hasselmann, and P. Kopietz, e-print arXiv:1008.4521.
12. L. P. Kadanoff, Physics (Long Island City, N.Y.) 2, 263 (1966).
13. A. Parola and L. Reatto, Adv. Phys. 44, 211 (1995). 10.1080/ 00018739500101536
14. V. L. Berezinskii, Sov. Phys. JETP 32, 493 (1970)
15. V. L. Berezinskii, Sov. Phys. JETP 34, 610 (1971).
16. J. M. Kosterlitz and D. J. Thouless, J. Phys. C 6, 1181 (1973). 10.1088/0022-3719/6/7/010
17. D. Litim, Phys. Lett. B 486, 92 (2000). 10.1016/S0370-2693(00)00748-6
18. Stricto sensu, the local limit of Hamiltonian corresponds to C = 0.
19. + 1 π d / 2 Γ (d / 2). Equation then reduces to the usual LPA equation derived in the continuum limit of model.
20. We omit a factor of T in the definition of the susceptibility.
21. U. Wolff, Phys. Lett. B 228, 379 (1989). 10.1016/0370-2693(89)91563-3
22. We use ln cosh argtanh x = - 1 2 ln (1 - x 2).
23. M. Hasenbusch and S. Meyer, Phys. Lett. B 241, 238 (1990). 10.1016/0370-2693(90)91286-K
24. C. Holm and W. Janke, Phys. Rev. B 48, 936 (1993). 10.1103/PhysRevB.48. 936
25. J. W. Essam and M. E. Fisher, J. Chem. Phys. 38, 802 (1963). 10.1063/1.1733766
26. C. Bervillier, B. Boisseau, and H. Giacomini, Nucl. Phys. B 789, 525 (2008). 10.1016/j.nuclphysb.2007.07.005
27. L. Onsager, Phys. Rev. 65, 117 (1944). 10.1103/PhysRev.65.117
28. L. Canet, B. Delamotte, D. Mouhanna, and J. Vidal, Phys. Rev. D 67, 065004 (2003). 10.1103/PhysRevD.67.065004 (Pubitemid 44628766)
29. A. Parola and L. Reatto, Phys. Rev. Lett. 53, 2417 (1984). 10.1103/PhysRevLett.53.2417
30. G. Gianinetti and A. Parola, Phys. Rev. B 63, 104414 (2001). 10.1103/PhysRevB.63.104414
31. A. Parola, J. Phys. C 19, 5071 (1986). 10.1088/0022-3719/19/26/008
32. C. D. Ionescu, A. Parola, D. Pini, and L. Reatto, Phys. Rev. E 76, 031113 (2007). 10.1103/PhysRevE.76.031113 (Pubitemid 47443117)
33. A. Parola, D. Pini, and L. Reatto, e-print arXiv:0901.2064.
34. D. Pini, A. Parola, and L. Reatto, J. Stat. Phys. 72, 1179 (1993). 10.1007/BF01048185
35. J. M. Caillol, Mol. Phys. 104, 1931 (2006). 10.1080/00268970600740774 (Pubitemid 43869977)
36. J. M. Caillol, J. Phys. A 42, 225004 (2009). 10.1088/1751-8113/42/22/ 225004
37. M. Gräter and C. Wetterich, Phys. Rev. Lett. 75, 378 (1995). 10.1103/PhysRevLett.75.378
38. G. v. Gersdorff and C. Wetterich, Phys. Rev. B 64, 054513 (2001). 10.1103/PhysRevB.64.054513
39. P. Olsson, Phys. Rev. B 52, 4526 (1995). 10.1103/PhysRevB.52.4526
40. J.-P. Blaizot, R. Méndez-Galain, and N. Wschebor, Phys. Lett. B 632, 571 (2006). 10.1016/j.physletb.2005.10.086 (Pubitemid 43006016)
41. F. Benitez, J. P. Blaizot, H. Chaté, B. Delamotte, R. Méndez-Galain, and N. Wschebor, Phys. Rev. E 80, 030103 (R) (2009). 10.1103/PhysRevE.80.030103
42. Note that one could also take a system of decoupled clusters as the reference state in the lattice NPRG.
43. D. Yamamoto, Phys. Rev. B 79, 144427 (2009). 10.1103/PhysRevB.79.144427
44. W. Metzner and D. Vollhardt, Phys. Rev. Lett. 62, 324 (1989). 10.1103/PhysRevLett.62.324
45. A. Georges, G. Kotliar, W. Krauth, and M. J. Rozenberg, Rev. Mod. Phys. 68, 13 (1996). 10.1103/RevModPhys.68.13
46. M. H. Hettler, A. N. Tahvildar-Zadeh, M. Jarrell, T. Pruschke, and H. R. Krishnamurthy, Phys. Rev. B 58, R7475 (1998). 10.1103/PhysRevB.58.R7475
47. G. Kotliar, S. Y. Savrasov, G. Pálsson, and G. Biroli, Phys. Rev. Lett. 87, 186401 (2001). 10.1103/PhysRevLett.87.186401
48. C. Gros and R. Valentí, Phys. Rev. B 48, 418 (1993). 10.1103/PhysRevB.48.418
49. D. Sénéchal, D. Pérez, and M. Pioro-Ladrière, Phys. Rev. Lett. 84, 522 (2000). 10.1103/PhysRevLett.84.522
50. M. Potthoff, M. Aichhorn, and C. Dahnken, Phys. Rev. Lett. 91, 206402 (2003). 10.1103/PhysRevLett.91.206402
51. M. Potthoff, Eur. Phys. J. B 32, 429 (2003). 10.1140/epjb/e2003-00121-8 (Pubitemid 41201102)
52. A. Rançon and N. Dupuis (unpublished).