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Journal of Physics Conference Series

Phase Diagram of the Antiferromagnetic Blume-Capel Model on Triangular Lattice

Sojeong Park, Wooseop Kwak

Published Aug 1, 2016• 3 citations
Publisher

Abstract

We perform Monte-Carlo simulations of the anti-ferromagnetic (AF) spin-1 Blume- Capel (BC) model and the AF Ising model on triangular lattice. We estimate the exact critical magnetic fields for both models at zero temperature using the Wang-Landau sampling method. We also show the phase diagrams and the critical lines for the models using the joint density functions. We find that the shapes of critical lines for the models are identical, but the phase transitions across the critical lines are different.

DOI
10.1088/1742-6596/738/1/012126

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We perform Monte-Carlo simulations of the anti-ferromagnetic (AF) spin-1 Blume- Capel (BC) model and the AF Ising model on triangular lattice. We estimate the exact critical magnetic fields for both models at zero temperature using the Wang-Landau sampling method. We also show the phase diagrams and the critical lines for the models using the joint density functions. We find that the shapes of critical lines for the models are identical, but the phase transitions across the critical lines are different.
Abstract We investigate the density of states (DOS) in an antiferromagnetic spin‐system on a square lattice described by the Blume–Capel (BC) model. We use a new and very efficient simulation method, proposed by Wang and Landau, in which we estimate very precisely DOS by sampling in the space of energy. Then we calculate the thermodynamical averages like internal energy, free energy, specific heat and entropy. The BC model exhibits multicritical behaviour such as first‐ or second‐order transitions and tricritical points. It is known that the ground state of the model can exhibit two kinds of staggered antiferromagnetic phases: AF 1 (two interpenetrating lattices with S = –1 and S = 1) and AF 2 ( S = –1 and S = 0 for H < 0; S = 1 and S = 0 for H > 0). We analyze the coexistence of such phases at finite temperatures and determine border lines between them. To understand the microscopic nature of such boundaries we present also some results obtained with the standard Monte Carlo method. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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.
Phase diagram and critical phenomena of a frustrated Blume–Capel model with alternating single-ion anisotropy ±D, nearest- and next-nearest-neighbour exchange interactions with equal magnitude J are studied by the Monte Carlo simulations using Wang–Landau sampling and nonequilibrium relaxation method. The collinear ordered phase due to next-nearest-neighbour interaction and partial ordered phase due to alternating anisotropy are confirmed together with a paramagnetic phase. We obtained the numerical results which strongly suggests that a single phase transition at D=0 splits into two Ising lines as soon as D is switched on. With the increase of D, the critical point of the easy-axis sublattice stays on a usual Ising-like critical line while that of the easy-plane sublattice passes through the tricritical point and the transition becomes of the first order as in the usual Blume–Capel model.
We use a thermodynamically self-consistent theory to obtain the phase diagram of the ferromagnetic spin-3/2 Blume-Capel model on the simple cubic lattice. The theory is based on an Ornstein-Zernike approximation where the direct correlation function is truncated and the dependence upon the thermodynamic variables is determined by a set of two coupled partial differential equations. Within this framework, we localize the critical line in zero external field with high accuracy and in good agreement with previous Monte Carlo analysis. At low temperature, in contrast with Monte Carlo results, we find a first-order transition line ending at a critical end point whose coordinates are given by (k(B)T(c)/Jc=0.213+/-0.003,Delta(c)/Jc=0.491+/-0.001).
We have studied the phase diagrams of the one-dimensional spin-1 Blume-Capel model with anisotropy constant D, in which equivalent-neighbor ferromagnetic interactions of strength -J are superimposed on nearest-neighbor antiferromagnetic interactions of strength K. A rich critical behavior is found due to the competing interactions. At zero temperature two ordered phases exist in the D/J-K/J plane, namely the ferromagnetic (F) and the antiferromagnetic one (AF). For lower values of D/J(D/J<0.25) these two ordered phases are separated by the point K_{c}=0.25J. For 0.25<D/J≤0.50, the paramagnetic phase P emerges in a region separated between the lines determined by D/J=0.5-K/J and D/J=K/J. For D/J>0.5, only phases AF and F exist and are separated by a line given by D/J=K/J. At finite temperatures, we found that the ferromagnetic region of the phase diagram in the k_{B}T/J-D/J plane is enriched by another ferromagnetic phase F^{^{'}} above a first-order line for 0.195<K/J<0.250. This first-order line, which separates phases F and F^{^{'}}, begins at a coexistence point, where phases F,F^{^{'}}, and P coexist, and ends at an ordered critical point. Similarly, we found that the phase F^{^{'}} is present in the phase diagram in the k_{B}T/J-K/J plane for 0.228<D/J<0.286.