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Communications in Theoretical Physics

The Critical Behavior of the Ising Model on Union Jack Lattice

Fu-Gao Wang, Jia-Zhen Hu

Published Sep 15, 1996• 0 citations
Publisher

Abstract

In this paper, we have investigated the critical behavior of the ferromagnetic Ising model on union jack lattice. The model is equivalent to the eight-vertex model which can be solved as a free fermion model with the free fermion approximation. The critical exponents have been obtained as and .
DOI
10.1088/0253-6102/26/2/175

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Abstract The mixed spin‐1/2 and spin‐3/2 Ising model on the Union Jack lattice is solved by establishing a mapping correspondence with the eight‐vertex model. It is shown that the model under investigation becomes exactly soluble as a free‐fermion eight‐vertex model when the parameter of uniaxial single‐ion anisotropy tends to infinity. Under this restriction, the critical points are characterized by critical exponents from the standard Ising universality class. In a certain subspace of interaction parameters, which corresponds to a coexistence surface between two ordered phases, the model becomes exactly soluble as a symmetric zero‐field eight‐vertex model. This surface is bounded by a line of bicritical points having interaction‐dependent critical exponents that satisfy a weak universality hypothesis. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)