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Physical review. B, Condensed matter

Ising model with competing axial interactions in the presence of a field: A renormalization-group treatment

Carlos S. O. Yokoi, Mauricio D. Coutinho-Filho, Silvio R. A. Salinas

Published Apr 1, 1985• 8 citations
Publisher

Abstract

On the basis of an \ensuremath{\epsilon} expansion, we present a renormalization-group analysis of the anisotropic next-nearest-neighbor Ising model in a field. For small fields, the \ensuremath{\gamma} surface remains XY-like. For larger fields, we confirm the existence of lines of tricritical points which are governed by Gaussian-type exponents. We pay special attention to the many couplings between a two-component critical spin field, associated with the main harmonic component of the magnetization, and several noncritical spin fields, associated with the uniform and the higher harmonic components. We remark that it is necessary to take into account the uniform and the second-harmonic components of the magnetization to describe the tricritical behavior.

DOI
10.1103/physrevb.31.4502

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On the basis of an \ensuremath{\epsilon} expansion, we present a renormalization-group analysis of the anisotropic next-nearest-neighbor Ising model in a field. For small fields, the \ensuremath{\gamma} surface remains XY-like. For larger fields, we confirm the existence of lines of tricritical points which are governed by Gaussian-type exponents. We pay special attention to the many couplings between a two-component critical spin field, associated with the main harmonic component of the magnetization, and several noncritical spin fields, associated with the uniform and the higher harmonic components. We remark that it is necessary to take into account the uniform and the second-harmonic components of the magnetization to describe the tricritical behavior.
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The authors study the Ising model on the triangular lattice with nearest-neighbor couplings K(nn) , next-nearest-neighbor couplings K(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(nn) <0 , but we also explore the ferromagnetic regime K(nn) >/=0 for H=0 . For K(nn) <0 and H=0 we locate a critical phase presumably covering the whole range -infinity< K(nn) <0 . For K(nn) <0 , H not equal 0 we locate a plane of phase transitions containing a line of tricritical three-state Potts transitions. In the limit H-->infinity this line leads to a tricritical model of hard hexagons with an attractive next-nearest-neighbor potential.