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Journal of Physics A Mathematical and General

Ising transition in the classical ANNNXY model

Pascal Simon

Published Apr 21, 1997• 13 citations
Publisher

Abstract

We investigate the XY model with ferromagnetic nearest and antiferromagnetic next-to-nearest neighbours couplings (ANNNXY model). We formulate the study of both phases of the model in terms of different Coulomb gas models. The non-frustrated ferromagnetic phase is thus transformed into a usual Coulomb gas with one species, whereas the frustrated phase is translated into a Coulomb gas with three species interacting with each other in an anisotropic lattice. We then generalize the Kosterlitz - Thouless renormalization group equations for both phases by treating the Ising and Kosterlitz - Thouless order parameters in an independent way. This enables us to discuss the nature of the transition (Ising and (or) Kosterlitz - Thouless) in the frustrated phase.

DOI
10.1088/0305-4470/30/8/013

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A two-dimensional triangular Ising lattice with the nearest-neighbor antiferromagnetic interaction J 1 and the next-nearest-neighbor ferromagnetic interaction - J 2 is studied by the Monte Carlo simulation. It is shown that the system with a finite J 2 undergoes the successive phase transition, paramagnetic→Kosterlitz-Thouless (KT)-like→ferrimagnetic phases, as temperature decreases. The sub-lattice switching phenomenon observed in our previous work is shown to be an intrinsic property inherent to the present system which has an XY character. The marginal exponent of the order-parameter correlation function at the KT-like transition point is seen to increase from 1/4 as the ratio J 2 / J 1 decreases, namely, it reveals a deviation from the universal behavior of a genuine XY model.
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