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Journal of Physics A Mathematical and General

Relations for polarization exponents (in magnetic lattice theory)

Ian Graham Enting

Published Oct 1, 1975• 11 citations
Publisher

Abstract

It is pointed out that the eight-vertex model, the triplet model and the Ashkin-Teller (1943) model have a common exponent relation beta e = 1 / 4 - 1 / 4 alpha that is not a consequence of scaling theory. It is proposed that this relation reflects a special symmetry of these models and this proposal is related to possible classification of two-dimensional systems.

DOI
10.1088/0305-4470/8/10/020

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It is pointed out that the eight-vertex model, the triplet model and the Ashkin-Teller (1943) model have a common exponent relation beta e = 1 / 4 - 1 / 4 alpha that is not a consequence of scaling theory. It is proposed that this relation reflects a special symmetry of these models and this proposal is related to possible classification of two-dimensional systems.
It is widely believed that the critical properties of several planar lattice models, like the Eight Vertex or the Ashkin-Teller models, are well described by an effective Quantum Field Theory obtained as formal scaling limit. On the basis of this assumption several extended scaling relations among their indices were conjectured. We prove the validity of some of them, among which the ones by Kadanoff, [13], and by Luther and Peschel, [16]. 1 Introduction and main results Integrable models in statistical mechanics, like the Ising or the Eight vertex (8V) models in two dimensions, provide conceptual laboratories for the understanding of phase transitions. Integrability is however a rather delicate property requiring very special features, and it is usually lost in more realistic models.