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physica status solidi (b)

Tricritical Behaviour in Correlated Effective Field Theory

S. Mukhopadhyay, Ibha Chatterjee

Published Apr 1, 1988• 1 citation
Publisher

Abstract

Abstract Correlated effective field theory is applied to study the tricritical behaviour for a Blume‐Capel type of Hamiltonian as well as for a Hamiltonian with antiferromagnetic nearest neighbour and ferromagnetic next nearest neighbour interactions. Two different regions in the phase‐diagram are identified by estimating the slope of the double log plot of order parameter and reduced temperature. It clearly indicates that a tricritical region appears when the ratio of two competing parameters exceeds a critical value.

DOI
10.1002/pssb.2221460232

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Abstract Correlated effective field theory is applied to study the tricritical behaviour for a Blume‐Capel type of Hamiltonian as well as for a Hamiltonian with antiferromagnetic nearest neighbour and ferromagnetic next nearest neighbour interactions. Two different regions in the phase‐diagram are identified by estimating the slope of the double log plot of order parameter and reduced temperature. It clearly indicates that a tricritical region appears when the ratio of two competing parameters exceeds a critical value.
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Using a Monte Carlo renormalization-group (MCRG) method we study tricritical behavior in two very different two-dimensional spin models: the Blume-Capel ferromagnet and the next-nearest-neighbor Ising antiferromagnet. The MCRG method is used to locate accurately tricritical points independent of the convergence of eigenvalue estimates. Despite the different symmetries and the different renormalization transformations used for the two models, in both cases we find four relevant tricritical eigenvalues which are essentially identical for both models. For the antiferromagnet, there is no indication of any decomposition of the tricritical point as predicted by mean-field theory, for ratios of intrasublattice to intersublattice coupling as small as (1/8).
The tricritical points on the nearest neighbour interaction mixed spin-½ and spin-1 transverse Ising system with a crystal field are investigated within the framework of the effective field theory (EFT) with correlations. Particular emphasis is given to the square lattice for which phase diagrams are obtained. If the transverse field varies in certain ranges, we find that tricritical points are obtained for the present system. The effect of the transverse field on the behaviour of the tricritical points is discussed in this paper.