Partition function zeroes of a self-dual Ising model

Physica A: Statistical Mechanics and its Applications

Volumn 258, Issue 1-2, 1998, Pages 157-170

  Lu, Wentao T ^a   Wu, F Y ^a  

^a NORTHEASTERN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; MATHEMATICAL MODELS; POLES AND ZEROS; POLYNOMIALS;

ISING MODEL; PARTITION FUNCTION ZEROES;

FERRIMAGNETIC MATERIALS;

EID: 0032166428     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-4371(98)00273-8     Document Type: Article

References (13)

1. C.N. Yang, T.D. Lee, Phys. Rev. 87 (1952) 404.
2. M.E. Fisher, in: W.E. Brittin (Ed.), Lecture Notes in Theoretical Physics, vol. 7c, University of Colorado Press, Boulder, 1965.
3. Historically, a systemic study of the zeroes of the Ising partition function in the thermodynamic limit was first carried by Stephenson. See, J. Stephenson, Physica A 148 (1988) 107, and references cited therein.
4. More recently, zeroes of the Potts model including those of the Ising model have been studied extensively by R. Shrock and co-workers using enumerations techniques and low-temperature expansions. See, V. Matveev, R. Shrock, Phys. Rev. E 54 (1996) 6174 and references cited therein.
5. For a numerical study of the Potts zeroes, see C.N. Chen, C.K. Hu, F.Y. Wu, Phys. Rev. Lett. 76 (1996) 169, and references cited therein.
6. Z. Glumac, K. Uzelac, J. Phys. A 27 (1994) 7709; F.Y. Wu, preprint cond-mat/9805 301.
7. Z. Glumac, K. Uzelac, J. Phys. A 27 (1994) 7709; F.Y. Wu, preprint cond-mat/9805 301.
8. Eq. (3) follows from the fact that to each closed polygonal configuration in ℒ there exist two closed polygonal configurations in ℒ*, obtained by completing the polygons along the innermost circle in two different ways. These two configurations carry the same weight since the edge weight for the innermost circle is 1.
9. P.W. Kasteleyn, Physica 27 (1961) 1209.
10. B.M. McCoy, T.T. Wu, The Two-dimensional Ising Model, Harvard University Press, 1973.
11. B.M. McCoy, T.T. Wu, Phys. Rev. 162 (1967) 436.
12. See, for example, I.S. Gradshteyn, I.M. Ryzhik, Tables of Integrals, Series, and Products, Academic Press, New York, 1965, p. 34, 1.394 with x = y = 1 and a = -π/n.
13. Note that in comparing the two results, the caption of Fig. 19.1 of [2] contains a misprint where v= tanh(K/2) should read v=tanh K.