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Journal of Physics A Mathematical and General

Honeycomb Ising antiferromagnet in a magnetic field: interface tension and critical temperature

Noriko Akutsu, Y Akutsu

Published Mar 7, 1990• 2 citations
Publisher

Abstract

By extending the method due to Muller-Hartmann and Zittartz (1977), the authors calculate the interface tension for the nearest-neighbour antiferromagnetic Ising model on the honeycomb lattice at finite magnetic fields. The calculation reproduces exact interface tension at zero field. From the zero point of the interface tension they derive a compact analytic form of the 'critical frontier' in the (H, T) plane (H: magnetic field, T: temperature), which agrees excellently with the recent 'quasi-analytical' result presented by Wu, Wu and Blote (1989).

DOI
10.1088/0305-4470/23/5/006

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By extending the method due to Muller-Hartmann and Zittartz (1977), the authors calculate the interface tension for the nearest-neighbour antiferromagnetic Ising model on the honeycomb lattice at finite magnetic fields. The calculation reproduces exact interface tension at zero field. From the zero point of the interface tension they derive a compact analytic form of the 'critical frontier' in the (H, T) plane (H: magnetic field, T: temperature), which agrees excellently with the recent 'quasi-analytical' result presented by Wu, Wu and Blote (1989).
A closed-form expression is proposed for the critical frontier, or the critical line, of the antiferromagnetic Ising model on the honeycomb lattice in a nonzero external magnetic field. We formulate the Ising model as an 8-vertex model and identify the critical frontier as a locus invariant under a generalized weak-graph transformation. In its simplest form the locus is an expression containing two unknown constants which we determine numerically. The resulting critical frontier lies very close to results of a finite-size analysis.
In this paper we present highly accurate numerical results of the determination of the critical point of the antiferromagnetic Ising model in a nonzero magnetic field for the honeycomb lattice, including the critical fugacity of a nearest-neighbor exclusion lattice gas. We compute the correlation length of the Ising model using a transfer matrix approach, and locate the critical point from the data on the correlation lengths using finite-size analysis. For the purpose of a maximum numerical accuracy, the analysis is carried out by taking transfer matrices proceeding in two perpendicular directions of the lattice.