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Physical Review Letters

Exact Results for the Eight-Vertex Model in Three Dimensions

Bill Sutherland

Published Dec 17, 1973• 7 citations
Publisher

Abstract

A generalized duality argument, similar to the treatment of the two-dimensional Ising model by Kramers and Wannier, is used to locate the transition temperature of the eightvertex model in three dimensions.
DOI
10.1103/physrevlett.31.1504

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The 2D quantum phase transition that occurs in a square lattice of Josephson-coupled p +/- ip superconductors is an example of how four-body interactions in d = 2 reproduce nonperturbative effects caused by two-body interactions in d = 1. The ordered phase has an unconventional "bond order" of the local T-breaking variable. This problem can be analyzed using an exact self-duality; this duality in classical notation is the 3D generalization of the Kramers-Wannier duality of the 2D Ising model, and there are similar exact dualities in dimensions d > or = 3. We discuss the excitation spectrum and experimental signatures of the ordered and disordered phases, and the relationship between our model and previously studied behavior of 2D boson models with four-boson interactions.
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