Graphical representations and cluster algorithms II

Physica A: Statistical Mechanics and its Applications

Volumn 254, Issue 3-4, 1998, Pages 477-516

  Chayes, L ^a   Machta, J ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF MASSACHUSETTS   (United States)

Author keywords

Cluster algorithms; Random cluster models

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; GRAPHIC METHODS; MATHEMATICAL MODELS; PERCOLATION (FLUIDS); PHASE TRANSITIONS;

CLUSTER ALGORITHM; FORTUIN-KASTELEYN MODEL; RANDOM CLUSTER MODEL; RAPID SIMULATION; SWENDSEN-WANG ALGORITHM; WIDOM-ROWLINSON MODEL;

STATISTICAL MECHANICS;

EID: 0032097196     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-4371(97)00637-7     Document Type: Article

References (47)

1. L. Chayes, J. Machta, Graphical representations and cluster algorithms. I. Discrete spin systems, Physica A 239 (1997) 542-601.
2. C.M. Fortuin, P.W. Kasteleyn, On the random cluster model I. Introduction and relation to other models, Physica 57 (1972) 536-564.
3. R.H. Swendsen, J.S. Wang, Nonuniversal critical dynamics in Monte Carlo simulations, Phys. Rev. Lett. 58 (1987) 86.
4. R.G. Edwards, A.D. Sokal, Generalization of the Fortuin-Kasteleyn-Swendsen-Wang representation and Monte Carlo algorithm, Phys. Rev. D 38 (1988) 2009-2012.
5. J. Machta, Y.S. Choi, A. Lucke, T. Schweizer, L.V. Chayes, Invaded cluster algorithm for equilibrium critical points, Phys. Rev. Lett. 75 (1995) 2792-2795.
6. J. Machta, Y.S. Choi, A. Lucke, T. Schweizer, L.M. Chayes, Invaded cluster algorithm for Potts models, Phys. Rev. E 54 (1996) 1332-1345.
7. W. Klein, Potts-model formulation of continuum percolation, Phys. Rev. B 26 (1982) 2677-2678.
8. J.A. Givens, G. Stell, The Kirkwood-Salsburg equation for random continuum percolation, J. Stat. Phys. 59 (1980) 981-1018.
9. U. Wolff, Collective Monte Carlo updating for spin systems, Phys. Rev. Lett. 62 (1989) 361.
10. D. Kandel, E. Domany, General cluster Monte Carlo dynamics, Phys. Rev. B 43 (1991) 8539-8548.
11. 2 Ising and Potts models, J. Stat. Phys. 50 (1988) 1-40.
12. J.T. Chayes, L. Chayes, R. Kotecký, The Analysis of the Widom-Rowlinson model by stochastic geometric methods, Commun. Math. Phys. 172 (1995) 551-569.
13. G. Giacomin, J.L. Lebowitz, C. Maes, Agreement percolation and phase coexistence in some Gibbs systems, J. Stat. Phys. 22 (1995) 1379-1403.
14. The present work.
15. O. Häggström, M.N.M. Lieshout, J. Moller, Characterization results and Markov chain Monte Carlo algorithms including exact simulation for some spacial point processes, preprint, 1996.
16. H.-O. Georgii, O. Häggström, Phase transition in continuum Potts models, Commun. Math. Phys. 181 (1996) 507-528.
17. J. Salas, A.D. Sokal, Dynamic critical behavior of a Swendsen-Wang-type algorithm for the Ashkin-Teller model, J. Stat. Phys. 85 (1996) 297-361.
18. C.E. Pfister, Y. Velenik, Random cluster representation of the Ashkin-Teller model, J. Stat. Phys. 88 (1997) 1295-1331.
19. S. Wiseman, E. Domany, Cluster method for the Ashkin-Teller model, Phys. Rev. E 48 (1993) 4080-4090.
20. A. Patrascioiu, E. Seiler, Phase structure of two-dimensional spin models and percolation, J. Stat. Phys. 69 (1992) 573.
21. M. Aizenman, On the slow decay of O(2) correlations in the absence of topological excitations: remark on the Patrascioiu-Seiler model, J. Stat. Phys. 77 (1994) 351-359.
22. L. Chayes, Discontinuity of the spin-wave stiffness in the two-dimensional XY model, submitted.
23. M. Campbell, L. Chayes, The isotropic O(3) model and the Wolff representation, J. Phys. A: Math. Gen., to appear.
24. L. Chayes, R. Kotecký, S.B. Shlosman, Aggregation and intermediate phases in dilute spin-systems, Commun. Math. Phys. 171 (1995) 203-232.
25. G. Johnson, H. Gould, J. Machta, L.K. Chayes, Monte Carlo study of the Widom-Rowlinson fluid using cluster methods, preprint, 1997.
26. J. Machta, J. Jiang, L.X. Chayes, in preparation.
27. B. Bollobás, G. Grimmett, S. Janson, The random cluster model on the complete graph, Probab. Theory Related Fields 104 (1996) 283-317.
28. F.Y. Wu, Dilute Potts model, duality and site-bond percolation, J. Phys. A: Mathe. Gen. 14 (1981) L39-L44.
29. J.T. Chayes, L. Chayes, The correct extension of the Fortuin-Kasteleyn result to plaquette percolation, Nucl. Phys. B [FS] 235 (1984) 19-23.
30. G. Grimmett, Potts models and random-cluster processes with many-body interactions, J. Stat. Phys. 75 (1994) 67-121.
31. 4He mixtures, Phys. Rev. A 4 (1971) 1071-1077.
32. M. Aizenman, C.M. Newman, Commun. Math. Phys. 107 (1986) 611-647.
33. B. Widom, J.S. Rowlinson, New model for the study of liquid-vapor phase transitions, J. Chem. Phys. 52 (1970) 1670-1684.
34. J.L. Lebowitz, J.L. Monroe, Inequalities for higher order Ising spins and for continuum fluids, Commun. Math. Phys. 28 (1972) 301-311.
35. K.S. Alexander, L. Chayes, Non-perturbative criteria for Gibbsian uniqueness, Commun. Math. Phys., to appear.
36. L. Chayes, R. Kotecký, An intermediate phase for a classical continuum model, Phys. Rev. B 54 (1996) 9221-9224.
37. L. Chayes, D. Klein, A generalization of Poisson convergence to ́Gibbs convergencé with applications to statistical mechanics, Helv. Phys. Acta 67 (1994) 30-42.
38. See Ref. [36].
39. C. Heneley, preprint, 1996.
40. E. Domany, D. Mukamel, A. Schwimmer, Phase diagram of the ℤ(5) model on the square lattice, J. Phys. A: Math. Gen. 13 (1980) L311-L320.
41. B. Nienhuis, Coulomb gas formulation of two-dimensional phase transitions, in: C. Domb, J.L. Lebowitz (Eds.), Phase Transitions and Critical Phenomena, vol. 11, Academic Press, London, 1987.
42. D.B. Abraham, C.M. Newman, Wetting in a three-dimensional system: an exact solution, Phys. Rev. Lett. 61 (1988) 1969-1972.
43. H.G. Evertz, M. Hasenbusch, M. Marcu, K. Pinn, S. Solomon, Stochastic cluster algorithms for discrete Gaussian (SOS) models, Phys. Lett. B 254 (1991) 185-191.
44. M. Hasenbusch, G. Lana, M. Marcu, K. Pinn, Cluster algorithms for a solid-on-solid model with constraints, Phys. Rev. B 46 (1992) 10472-10475.
45. J.S. Wang, R.H. Swendsen, R. Kotecký, Antiferromagnetic Potts models, Phys. Rev. Lett. 63 (1989) 109-112.
46. J.S. Wang, R.H. Swendsen, R. Kotecký, 3-state antiferromagnetic Potts models - a Monte Carlo study, Phys. Rev. B 42 (1990) 2465-2474.
47. V. Rivasseau, Lieb's correlation inequality for plane roters, Commun. Math. Phys. 77 (1980) 145-147.