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arXiv:cond-mat/9703036 · Journal of the Physical Society of Japan

Free Energies and Critical Exponents of theA1(1),Bn(1),Cn(1)andDn(1)Face Models

Murray T. Batchelor, V. Fridkin, Atsuo Kuniba, Kazumitsu Sakai, Y. -K. Zhou

Published Apr 1, 1997• 5 citations
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Abstract

We obtain the free energies and critical exponents of models associated with elliptic solutions of the star-triangle relation and reflection equation.The models considered are related to the affine Lie algebras A (1)
DOI
10.1143/jpsj.66.913

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We obtain the free energies and critical exponents of models associated with elliptic solutions of the star-triangle relation and reflection equation.The models considered are related to the affine Lie algebrasn and D(1) n .The bulk and surface specific heat exponents are seen to satisfy the scaling relation 2α s = α b + 2. It follows from scaling relations that in regime III the correlation length exponent ν is given by ν = (l + g)/2g, where l is the level and g is the dual Coxeter number.In regime II we find ν = (l + g)/2l.
For pt.I see ibid, vol.17, p.1251 (1984). The authors continue their study of the star-triangle relation for two-component spin models, with the help of the inversion relation. The conclusion is that the most general interaction-round-a-face models (16 non-zero parameters) that satisfy the star-triangle relations are mainly Baxter (1972) and Fan and Wu (1970) models. In this way they recover Krichever's result (1981) for the classification of the star-triangle relations for vertex models. They sketch a generalisation of this approach to models with excluded configurations, to staggered models, and to three-dimensional models (tetrahedron relations).