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Journal of Physics A Mathematical and General

Equivalence of (d+1)-dimensional Ising systems of arbitrary spin to a d-dimensional spin-1/2quantum system

M B Green, Leigh Sneddon, Robin B. Stinchcombe

Published Jul 1, 1979• 4 citations
Publisher

Abstract

In a certain highly anisotropic limit the spin-S Ising model in d+1 dimensions is shown to be equivalent to the d-dimensional spin- 1 / 2 Ising model in a transverse field at zero temperature. This result relates, in the highly anisotropic limit, a group of models in the same universality class.
DOI
10.1088/0305-4470/12/7/008

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The partition function of a quantal spin system is expressed by that of the Ising model, on the basis of the generalized Trotter formula. Thereby the ground state of the d-dimensional Ising model with a transverse field is proven to be equivalent to the (d+1)-dimensional Ising model at finite temperatures. A general relationship is established between the two partition functions of a general quantal spin system and the corresponding Ising model with many-spin interactions, which yields some rigorous results on quantum systems. Some applications are given.