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Physical Review Letters

Critical Frontier of the Antiferromagnetic Ising Model in a Magnetic Field: The Honeycomb Lattice

Fa Yueh Wu, X. N. Wu, Henk W. J. Blöte

Published Aug 7, 1989• 3 citations
Publisher
DOI
10.1103/physrevlett.63.696.2

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Critical frontier of the antiferromagnetic Ising model in a magnetic field: The honeycomb lattice

Fa Yueh Wu, X. N. Wu, Henk W. J. Blöte

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.

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

Noriko Akutsu, Y Akutsu

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).

Journal of Physics A Mathematical and General•Mar 7, 1990•2 citations
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.
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).