A Monte Carlo sampling scheme for the Ising model

Journal of Statistical Physics

Volumn 114, Issue 1-2, 2004, Pages 455-480

  Häggkvist, Roland ^a   Rosengren, Anders ^b   Andrén, Daniel ^a   Kundrotas, Petras ^b,c   Lundow, Per Håkan ^b   Markström, Klas ^a  

^a UMEÅ UNIVERSITY   (Sweden)

^b ALBANOVA UNIVERSITY CENTER   (Sweden)

^c KAROLINSKA INSTITUTE   (Sweden)

Author keywords

Density of states; Microcanonical; Monte Carlo methods

Indexed keywords

EID: 3543026349     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/b:joss.0000003116.17579.5d     Document Type: Article

References (23)

1. E. Ising, Beitrag zur Theorie des Ferromagnetismus, Z. Physik 31:253-258 (1925).
2. L. Onsager, Crystal statistics I. A two-dimensional model with an order-disorder transition, Phys. Rev. 65:117-149 (1944).
3. B. A. Cipra, An introduction to the Ising model, Amer. Math. Monthly 94:937-959 (1987).
4. N. Metropolis, A. Rosenblut, M. Rosenbluth, A. Teller, and E. Teller, Equation of state calculation by fast computing machines, J. Chem. Phys. 21:1087-1092 (1953).
5. U. Wolff, Collective Monte Carlo updating for spin systems, Phys. Rev. Lett 62:361 (1989).
6. R. H. Swendsen and J.-S. Wang, Nonuniversal critical dynamics in Monte Carlo simulations, Phys. Rev. Lett. 58:86-88 (1987).
7. M. E. J. Newman and G. T. Barkema, Monte Carlo Methods in Statistical Physics (The Clarendon Press Oxford University Press, New York, 1999).
8. E. H. Lieb and Jakob Yngvason, The physics and mathematics of the second law of thermodynamics, Phys. Rep. 310:1-96 (1999).
9. R. Häggkvist and P. H. Lundow, The Ising partition function for 2D grids with cyclic boundary: Computation and analysis, J. Stat. Phys. 108:429-457 (2002). See also http://www.math.umu.se/~phl.
10. Roland Häggkvist, Anders Rosengren, Daniel Andrén, Petras Kundrotas, Per Håkan Lundow, and Klas Markström, On the 3-Dimensional Ising Model, manuscript.
11. P. H. Lundow and Klas Markström, A New Look at the Phase Transition of the 5-Dimensional Ising Model, manuscript.
12. P. M. C. de Oliveira, Broad histogram simulation; Microcanonical Ising dynamics, Int. J. Mod. Phys. C 3:497-503 (1998).
13. B. A. Berg and U. H. E. Hansmann, Configuration space for random walk dynamics, Eur. Phys. J. B 6:395-398 (1998).
14. J.-S. Wang and R. H. Swendsen, Transition matrix Monte Carlo method, J. Stat. Phys. 106:245-285 (2002).
15. Roland Häggkvist, Anders Rosengren, Daniel Andrén, Petras Kundrotas, Per Håkan Lundow, and Klas Markström, Exact Calcuclation of the Ising Partition Function for Large Square Grids, manuscript.
16. A. M. Ferrenberg and D. P. Landau, Critical behavior of the three-dimensional Ising model: A high-resolution Monte Carlo study, Phys. Rev. B 44:5081-5091 (1991).
17. D. P. Landau and K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics (Cambridge University Press, 2000).
18. J.-S. Wang and R. H. Swendsen, Transition Matrix Monte Carlo, arXiv:cond.mat/0104418 v1, 23 Apr 2001 (2001).
19. C. Borgs, J. Chayes, A. Frieze, J. H. Kim, P. Tetali, E. Vigoda, and V. Vu, Torpid Mixing of Some mcmc Algorithms in Statistical Physics, Proceedings of FOCS '99 (1999), pp. 218-229. Preprint available at http://www.math.cmu.edu/ ~af1p/papers.html.
20. F. Wang and M. Suzuki, Finite-size scaling properties of the damage distance and dynamical critical exponent for Ising model, Physica A 220:534-541 (1995).
21. F. Wang and D. P. Landau, Efficient, multiple-range random walk algorithm to calculate the density of states, Phys. Rev. Let. 86:2050-2053 (2001).
22. R. J. Baxter, Exactly Solved Models in Statistical Mechanics (Academic Press, 1982).
23. R. J. Baxter, Potts model at the critical temperature, J. Phys. C 6:L445-L448 (1973).