Cluster Monte Carlo simulation of the transverse Ising model

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 66, Issue 6, 2002, Pages 8-

  Blöte, Henk W J ^a,b   Deng, Youjin ^a  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b UNIVERSITEIT LEIDEN   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; ANISOTROPY; APPROXIMATION THEORY; ASPECT RATIO; BOUNDARY CONDITIONS; COMPUTER SIMULATION; EXTRAPOLATION; FUNCTIONS; HAMILTONIANS; MONTE CARLO METHODS; QUANTUM THEORY;

BINDER CUMULANT; ISING MODEL; PERIODIC BOUNDARY CONDITIONS (PBC); TRANSVERSE ISING MODEL (TIM);

MATHEMATICAL MODELS;

ARTICLE;

EID: 41349102123     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.66.066110     Document Type: Article

References (33)

1. T.D. Schultz, and D.C. Mattis, Rev. Mod. Phys. 36, 856 (1964).
2. M. Suzuki, Prog. Theor. Phys. 46, 1337 (1971).
3. M. Suzuki, Prog. Theor. Phys. 56, 2454 (1976).
4. H.F. Trotter, Proc. Am. Math. Soc. 10, 545 (1959).
5. R.P. Feynman, Statistical Mechanics (Benjamin, Reading, MA, 1972).
6. R.M. Stratt, Phys. Rev. B 33, 1921 (1986).
7. A. Wiesler, Phys. Lett. 89A, 352 (1982).
8. A continuous time algorithm for discrete quantum systems is due to B.B. Beard and U.-J. Wiese, Phys. Rev. Lett. 77, 5130 (1996);the present algorithm for the Ising model was presented by Henk W.J. Blöte at the Statphys 20 Conference, in Livre des Résumés, edited by A. Gervois, M. Gingold, and D. Iagolnitzer (UNESCO Sorbonne, Paris, 1998). A related algorithm of the Swendsen-Wang type was described in Ref. 30.
9. Y.J. Deng and H.W.J. Blöte, Phys. Rev. Lett. 88, 190602 (2002).
10. L. Onsager, Phys. Rev. 65, 117 (1944).
11. A.A. Migdal, Zh. Éksp. Teor. Fiz. 69, 1457 (1975) [Sov. Phys. JETP 42, 743 (1976)].
12. R.H. Swendsen and J.-S. Wang, Phys. Rev. Lett. 58, 86 (1987);
13. J.-S. Wang and R.H. Swendsen, Physica A 167, 565 (1990).
14. U. Wolff, Phys. Rev. Lett. 62, 361 (1989);
15. U. WolffPhys. Lett. B 228, 379 (1989).
16. E. Luijten and H.W.J. Blöte, Int. J. Mod. Phys. C 6, 359 (1995).
17. K. Binder, Z. Phys. B 43, 119 (1981).
18. G. Kamieniarz and H.W.J. Blöte, J. Phys. A 26, 201 (1992).
19. H.W.J. Blöte, E. Luijten, and J.R. Heringa, J. Phys. A 28, 6289 (1995).
20. R. Guida and J. Zinn-Justin, J. Phys. A 31, 8103 (1998).
21. H.W.J. Blöte, L.N. Schur, and A.L. Talapov, Int. J. Mod. Phys. C 10, 1137 (1999).
22. Y.J. Deng and H. W. J. Blöte (unpublished).
23. E. Luijten, Interaction Range, Universality and the Upper Critical Dimension (Delft University Press, Delft, 1997).
24. J.R. Heringa, H.W.J. Blöte, and E. Luijten, J. Phys. A 33, 2929 (2000).
25. E. Brézin and J. Zinn-Justin, Nucl. Phys. B 257, 867 (1985).
26. E.F. Samento and T. Kaneyoshi, J. Phys. C 21, 3933 (1988).
27. P.A. Slotte, J. Phys. A 20, L177 (1987).
28. Q. Jiang and Z.Y. Li, Phys. Rev. B 40, 11 264 (1989).
29. Q. Jiang and X.F. Jiang, Phys. Lett. A 224, 196 (1997).
30. R.J. Elliott and A.P. Young, Ferroelectrics 7, 23 (1974).
31. W.H. Zheng, J. Oitmaa, and C.J. Hamer, J. Phys. A 27, 5425 (1994).
32. R. Rieger and N. Kawashima, Eur. Phys. J. B 9, 233 (1999).
33. M.S.L. du Croo de Jongh and J.M.J. van Leeuwen, Phys. Rev. B 57, 8494 (1998).