The triangular Ising model with nearest- and next-nearest-neighbor couplings in a field

Abstract

We study the Ising model on the triangular lattice with nearest-neighbor couplings $K_{\mathrm{nn}}$, next-nearest-neighbor couplings $K_{\mathrm{nnn}}>0$, and a magnetic field $H$. This work is done by means of finite-size scaling of numerical results of transfer matrix calculations, and Monte Carlo simulations. We determine the phase diagram and confirm the character of the critical manifolds. The emphasis of this work is on the antiferromagnetic case $K_{\mathrm{nn}}<0$, but we also explore the ferromagnetic regime $K_{\mathrm{nn}}\ge 0$ for H=0. For $K_{\mathrm{nn}}<0$ and H=0 we locate a critical phase presumably covering the whole range $-\infty <K_{\mathrm{nn}}<0$. For $K_{\mathrm{nn}}<0$, $H\ne 0$ we locate a plane of phase transitions containing a line of tricritical three-state Potts transitions. In the limit $H\to \infty$ this line leads to a tricritical model of hard hexagons with an attractive next-nearest-neighbor potential.

References in corpus (3)

• Critical frontier of the triangular antiferromagnet in a field
• Search for Kosterlitz-Thouless transition in a triangular Ising antiferromagnet with further-neighbour ferromagnetic interactions
• Three-phase point in a binary hard-core lattice model?

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