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Physical review. B, Condensed matter

Multicritical behavior of the antiferromagnetic spin-3/2 Blume-Capel model: Finite-size-scaling and Monte Carlo studies

Smaîne Bekhechi, A. Benyoussef

Published Dec 1, 1997• 48 citations
Publisher

Abstract

Transfer-matrix finite-size-scaling calculations and Monte Carlo simulations are used to investigate the two-dimensional spin-3/2 Ising antiferromagnet in the presence of an external magnetic field and a single-ion potential. Comparison is made between the results of this study and previous mean-field calculations. The phase diagrams and the critical behavior of the model are discussed. In contrast to the mean-field picture, no decomposition of the tricritical point is observed.

DOI
10.1103/physrevb.56.13954

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Transfer-matrix finite-size-scaling calculations and Monte Carlo simulations are used to investigate the two-dimensional spin-3/2 Ising antiferromagnet in the presence of an external magnetic field and a single-ion potential. Comparison is made between the results of this study and previous mean-field calculations. The phase diagrams and the critical behavior of the model are discussed. In contrast to the mean-field picture, no decomposition of the tricritical point is observed.
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We study the two-dimensional, antiferromagnetic Blume-Capel model on a square lattice by numerical transfer-matrix and Monte Carlo finite-size scaling methods, in order to investigate whether the line of tricritical points in this model may be decomposed into lines of critical end points and double critical points, as predicted by mean-field theory and recent Monte Carlo simulations on a three-dimensional cubic lattice. Conclusive numerical evidence is obtained, indicating that such decomposition does u/Inot occur in this two-dimensional model. The nondecomposition is explained in terms of the large fluctuations in the two-dimensional nearest-neighbor model, and we speculate that the situation may be different in two-dimensional antiferromagnetic models with weak, ferromagnetic next-nearest-neighbor interactions.
We report on numerical simulations of the two-dimensional spin-1 Blume-Capel ferromagnet embedded in a triangular lattice. Utilizing a range of Monte Carlo and finite-size scaling techniques, we explore several critical aspects along the crystal field–temperature ( Δ , T ) transition line. Wang-Landau simulations measuring the joint density of states in combination with the method of field mixing allow us to probe the phase coexistence curve in high resolution, determining the tricritical point ( Δ t , T t ) with improved accuracy and verifying the tricritical exponents. Extensive multicanonical simulations identifying transition points across the phase diagram characterize the Ising universality class for Δ < Δ t with precise determination of thermal and magnetic critical exponents expected in the second-order regime. On the other hand, for Δ > Δ t , a finite-size scaling analysis is dedicated to revealing the first-order signature in the surface tension that linearly increases upon lowering the temperature deeper into the first-order transition regime. Finally, a comprehensive picture of the phase diagram for the model is presented, collecting transition points obtained from the combined numerical approach in this study and previous estimates in the literature.
The phase diagram of the two-dimensional Blume-Capel model is investigated by using the technique of phenomenological finite-size scaling. The location of the tricritical point and the values of the critical and tricritical exponents are determined. The location of the tricritical point (Tt{T}_{t}Tt​=0.610\ifmmode\pm\else\textpm\fi{}0.005, Dt{D}_{t}Dt​=1.9655\ifmmode\pm\else\textpm\fi{}0.0010) is well outside the error bars for the value quoted in previous Monte Carlo simulations but in excellent agreement with more recent Monte Carlo renormalization-group results. The values of the critical and tricritical exponents, with the exception of the leading thermal tricritical exponent, are in excellent agreement with previous calculations, conjectured values, and Monte Carlo renormalization-group studies.
The phase diagram and the critical behavior of the spin-1 and the spin-3/2 two-dimensional Baxter-Wu model in a crystal field are studied by conventional finite-size scaling and conformal invariance theory. The phase diagram of this model, for the spin-1 case, is qualitatively the same as those of the diluted 4-states Potts model and the spin-1 Blume-Capel model. However, for the present case, instead of a tricritical point one has a pentacritical point for a finite value of the crystal field, in disagreement with previous work based on finite-size calculations. On the other hand, for the spin-3/2 case, the phase diagram is much richer and can present, besides a pentacritical point, an additional multicritical end point. Our results also support that the universality class of the critical behavior of the spin-1 and spin-3/2 Baxter-Wu model in a crystal field is the same as the pure Baxter-Wu model, even at the multicritical points.