Abstract
In a previous paper we considered an extension of the hard hexagon model to a solvable two-dimensional lattice gas with at most two particles per pair of adjacent sites. Here we use various mathematical identities (in particular Gordon's generalization of the Rogers-Ramanujan relations) to express the local densities in terms of elliptic functions. The critical behavior is then readily obtained.
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R. J. Baxter and G. E. Andrews,J. Stat. Phys. 44:249 (1986).
R. J. Baxter,J. Phys. A. 13:L61 (1980);J. Stat. Phys. 26:427 (1981).
L. J. Rogers,Proc. Lond. Math. Soc. 25:318 (1894).
S. Ramanujan,Proc. Camb. Phil. Soc. 19:214 (1919).
B. Gordon,Am. J. Math. 83:393 (1961).
A. Kuniba, Y. Akutsu, and M. Wadati,J. Phys. Soc. Japan. 55:1092, and to appear (1986).
G. E. Andrews, R. J. Baxter, and P. J. Forrester,J. Stat. Phys. 35:193 (1984).
G. E. Andrews,The Theory of Partitions (Addison-Wesley, Reading, Massachusetts, 1976).
R. J. Baxter,Exactly Solved Models in Statistical Mechanics (Academic, London, 1982).
I. S. Gradshteyn and I. M. Ryzhik,Table of Integrals, Series and Products (Academic, New York, 1965).
D. A. Huse,Phys. Rev. B 30:3908 (1984).
D. A. Huse,Phys. Rev. Lett. 49:1121 (1982).
R. J. Baxter and P. A. Pearce,J. Phys. A 16:2239 (1983).
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Supported in part by the National Science Foundation Grant MCS 8201733.
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Andrews, G.E., Baxter, R.J. Lattice gas generalization of the hard hexagon model. II. The local densities as elliptic functions. J Stat Phys 44, 713–728 (1986). https://doi.org/10.1007/BF01011904
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DOI: https://doi.org/10.1007/BF01011904