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Journal of Physics A Mathematical and General

Z(N) generalisation of the Baxter-Wu model

Francisco Castilho Alcaraz, L Jacobs

Published Jul 1, 1982• 8 citations
Publisher

Abstract

A two-dimensional model of the dynamics of Z(N) spins on a triangular lattice with three-body interactions is analysed. The properties of the model under duality are shown to be identical to those of a wide class of models in two, three and four dimensions. Monte Carlo simulations reveal the existence of three phases for N>4, with an intermediate phase which is most likely soft.

DOI
10.1088/0305-4470/15/7/006

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Monte Carlo studies of the Z(4)Z(4)Z(4) (or Ashkin-Teller) model on the triangular lattice were carried out. In particular, we investigated whether the massless phase, which was shown to exist on the boundary of the physical parameter space, may extend into a region of finite width. The existence of such a phase would imply that Nc{N}_{c}Nc​, the critical value above which Z(N)Z(N)Z(N) models have intermediate phases, is nonuniversal, i.e., lattice and interaction dependent. Although, on the basis of our Monte Carlo results we cannot completely rule out this possibility, most aspects of our findings indicate consistency with existing theories of the Z(4)Z(4)Z(4) model which exclude the possibility of such an intermediate massless phase.