The Ising partition function for 2D grids with periodic boundary: Computation and analysis

Journal of Statistical Physics

Volumn 108, Issue 3-4, 2002, Pages 429-457

  Häggkvist, Roland ^a   Lundow, Per Håkan ^b  

^a UMEÅ UNIVERSITY   (Sweden)

^b ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

2D Ising model; Exact computation; External non zero field; Partition function; Transfer matrix

Indexed keywords

EID: 0141450302     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1015721706350     Document Type: Article

References (18)

1. B. A. Cipra, An introduction to the Ising model, Amer. Math. Monthly 94:937-959 (1987).
2. P. Beale, Exact distribution of energies in the two-dimensional Ising model, Phys. Rev. 76:78-81 (1996).
3. P. H. Lundow, Compression of transfer matrices. Technical Report 5 (Department of Mathematics, Umeå University, 1999).
4. P. H. Lundow, Computation of the Ising partition function for grid graphs. Technical Report 14 (Department of Mathematics, Umeå University, 1999).
5. G. A. Baker, The Markov property method applied to Ising model calculations, J. Stat. Phys. 77:955-976 (1994).
6. N. Biggs, Interaction Models (Cambridge University Press, 1977).
7. D. Babic et al., The matching polynomial of a polygraph, Discrete Appl. Math. 15:11-24 (1986).
8. P. H. Lundow, Multiprecision integers: A Fortan 90 module. Manuscript, 2000.
9. P. H. Lundow, Polynomials: A Fortran 90 module. Manuscript, 2000.
10. C. J. Thompson, Mathematical Statistical Mechanics (Princeton University Press, 1972).
11. B. M. McCoy and T. T. Wu, The Two-Dimensional Ising Model (Harvad University Press, 1973).
12. D. A. Lavis and G. M. Bell, Statistical Mechanics of Lattice Systems (Springa, 1999).
13. L. Onsager, Crystal statistics I. A two-dimensional model with an order-disorder transition. Phys. Rev. (2) 65:117-149 (1944).
14. C. Domb, Ising Model, in Phase Transitions and Critical Phenomena, Vol. 3, C. Domb and M. S. Green, eds. (Academic Press, 1972).
15. K. Binder, Finite size scaling analysis of Ising model block distribution functions, Z. Phys. B-condensed matter 43:119-140 (1981).
16. M. N. Barber, Finite-size scaling, in Phase Transitions and Critical Phenomena, Vol. 8, C. Domb and J. L. Lebowitz, eds. (Academic Press, 1983).
17. X. P. Kong, H. Au-Yang, and H. H. Perk, Logarithmic Singularities of Q-dependent susceptibility, Phys. Letts. A, 118:336-340 (1986).
18. R. Häggkvist and A. Rosengren, Some conjectures concerning the coefficients in the Ising polynomial. Manuscript, 1997.