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Journal of Physics C Solid State Physics

The transverse Ising model in the paid approximation

Terufumi Yokota

Published Dec 20, 1988• 19 citations
Publisher

Abstract

The transverse Ising model is investigated in the pair approximation. Critical lines for an arbitrary number of nearest-neighbour spins can be obtained. Using the approximation, Suzuki's coherent anomaly method is applied to the model and critical exponents of the susceptibility are estimated and compared with the real values. The agreement is not excellent for the small size of the cluster used and the author concludes that larger clusters are necessary for a reliable estimate for the critical exponents by this method.

DOI
10.1088/0022-3719/21/35/019

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Progress of Theoretical Physics Supplement•Jan 1, 1994•2 citations
The transverse Ising model is investigated in the pair approximation. Critical lines for an arbitrary number of nearest-neighbour spins can be obtained. Using the approximation, Suzuki's coherent anomaly method is applied to the model and critical exponents of the susceptibility are estimated and compared with the real values. The agreement is not excellent for the small size of the cluster used and the author concludes that larger clusters are necessary for a reliable estimate for the critical exponents by this method.
The Ising model with a transverse field has been investigated for both positive and negative exchange interactions. Effective Hamiltonians are used for a pair of nearest-neighbour spins. The transition temperature and susceptibility above the transition temperature are calculated. The critical magnitude of the transverse field for which the transition temperature becomes 0 K is also evaluated. When the transverse field is absent, the result of the present method is reduced to that of the Bethe approximation.
The correlation length of the Ising model on the simple cubic lattice is calculated directly from the magnetization profiles which are determined in the pair, the square, and the cube approximations in the simplified cluster variation method. The critical exponent ν is obtained by applying the coherent anomaly method to the correlation length. The wave-number dependent magnetic susceptibility or the spin-pair correlation function is not required in obtaining the expression for the correlation length.
The spin-pair correlation functions in the Ising model with nearest-neighbor interaction J>0 and next-nearest-neighbor interaction J′ on the square lattice are obtained in three approximations of the simplified cluster variation method. We estimate the critical indices ην, γ and ν, by applying the coherent-anomaly method to the obtained spin-pair correlation functions. We conclude that the system belongs to the Onsager universality class when J′/J > −0.5 and does not when J′/J < −0.5.