Calculations of the dynamical critical exponent using the asymptotic series summation method

Theoretical and Mathematical Physics

Volumn 147, Issue 1, 2006, Pages 561-575

  Krinitsyn, A S ^a   Prudnikov, V V ^a   Prudnikov, P V ^a  

^a OMSK STATE UNIVERSITY   (Russian Federation)

Author keywords

Asymptotic series; Critical dynamics; Dynamical critical exponent; Renormalization group; Summation methods

Indexed keywords

EID: 33646001432     PISSN: 00405779     EISSN: 15739333     Source Type: Journal    
DOI: 10.1007/s11232-006-0063-z     Document Type: Article

References (46)

1. P. C. Hohenberg and B. I. Halperin, Rev. Modern Phys., 49, 435 (1977).
2. R. Bausch, H. K. Janssen, and H. Wagner, Z. Phys. B, 24, 113 (1976);
3. C. De Dominicis, E. Brézin, and J. Zinn-Justin, Phys. Rev. B, 12, 4945 (1975);
4. N. V. Antonov and A. N. Vasil'ev, Theor. Math. Phys., 60, 671 (1984);
5. B. I. Halperin, P. C. Hohenberg, and S. Ma, Phys. Rev. Lett., 29, 1548 (1972);
6. B. I. Halperin, P. C. Hohenberg, E. D. Siggia, and S. Ma, Phys. Rev. B, 13, 2110 (1976).
7. V. V. Prudnikov and A. N. Vakilov, JETP, 74, 990 (1992).
8. V. V. Prudnikov, A. V. Ivanov, and A. A. Fedorenko, JETP Letters, 66, 835 (1997).
9. V. V. Prudnikov et al., JETP, 87, 527 (1998).
10. G. A. Baker, B. G. Nickel, M. S. Green, and D. I. Meiron, Phys. Rev. Lett., 36, 1351 (1976);
11. Phys. Rev. B, 17, 1365 (1978).
12. J. C. Le Guillou and J. Zinn-Justin, Phys. Rev. Lett., 39, 95 (1977);
13. Phys. Rev. B, 21, 3976 (1980).
14. S. A. Antonenko and A. I. Sokolov, Phys. Rev. B, 51, 1894 (1995).
15. A. Pelissetto and E. Vicari, Phys. Rev. B, 62, 6393 (2000).
16. J. Zinn-Justin, Quantum Field Theory and Critical Phenomena, Clarendon, Oxford (1996);
17. A. N. Vasil'ev, Quantum-Field Renormalization Group in the Theory of Critical Phenomena and Stochastic Dynamics [in Russian], PNPI, St. Petersburg (1998); English transl. CRC Press, Boca Raton, F1. (2004).
18. V. S. Dotsenko, Phys. Usp., 138, 457 (1995).
19. L. N. Lipatov, JETP, 45, 216 (1977).
20. E. Brézin, J. C. Le Guillou, and J. Zinn-Justin, Phys. Rev. D, 15, 1544 (1977).
21. G. H. Hardy, Divergent Series, Clarendon, Oxford (1949);
22. D. I. Kazakov, O. V. Tarasov, and D. V. Shirkov, Theor. Math. Phys., 38, 9 (1979);
23. D. I. Kazakov and V. S. Popov, JETP, 95, 581 (2002);
24. I. M. Suslov, JETP, 93, 1 (2001).
25. J. Honkonen, M. V. Komarova, and M. Yu. Nalimov, Nucl. Phys. B, 714, 292 (2005);
26. Nucl. Phys. B, 707, 493 (2005); hep-th/0406168 (2004).
27. C. M. Bender and T. T. Wu, Phys. Rev., 184, 1231 (1969).
28. J. Čížek and E. R. Vrscay, Int. J. Quant. Chem., 21, 27 (1982).
29. D. P. Belanger et al., Journ. de Phys., 49, C8-1229 (1988).
30. R. B. Pearson, J. L. Richardson, and D. Toussaint, Phys. Rev. B, 31, 4472 (1985).
31. V. V. Prudnikov and A. N. Vakilov, JETP, 76, 469 (1993).
32. S. Wansleben and D. P. Landau, Phys. Rev. B, 43, 6006 (1991).
33. U. Gropengiessen, Phys. A, 213, 308 (1995).
34. P. Grassberger, Phys. A, 214, 547 (1995).
35. C. Kalle, J. Phys. A, 17, L801 (1984).
36. J. K. Williams, J. Phys. A, 18, 49 (1985).
37. M. Mori and Y. Tsuda, Phys. Rev. B, 37, 5444 (1988).
38. P. H. Poole and N. Jan, J. Phys. A, 23, L453 (1990).
39. V. V. Prudnikov and O. N. Markov, Europhys. Lett., 29, 245 (1995).
40. F. Wang, N. Hatane, and M. Suzuki, J. Phys. A, 28, 4543 (1995).
41. M. P. Nightingale and H. W. J. Blöte, Phys. Rev. B, 62, 1089 (2000).
42. Z. Racz and M. F. Collins, Phys. Rev. B, 13, 3074 (1976).
43. H.-O. Heuer, J. Phys. A, 26, L341 (1993).
44. G. Parisi, F. Ricci-Tersenghi, and J. J. Ruiz-Lorenzo, Phys. Rev. E, 60, 5198 (1999).
45. H. G. Ballesteros et al., Phys. Rev. B, 58, 2740 (1998).
46. N. Rosov, C. Hohenemser, and M. Eibschutz, Phys. Rev. B, 46, 3452 (1992).