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International Journal of Modern Physics C

TWO-DIMENSIONAL WANG–LANDAU SAMPLING OF AN ASYMMETRIC ISING MODEL

Shan-Ho Tsai, Fugao Wang, David Paul Landau

Published Sep 1, 2009• 2 citations
Publisher

Abstract

We study the critical endpoint behavior of an asymmetric Ising model with two- and three-body interactions on a triangular lattice, in the presence of an external field. We use a two-dimensional Wang–Landau sampling method to determine the density of states for this model. An accurate density of states allowed us to map out the phase diagram accurately and observe a clear divergence of the curvature of the spectator phase boundary and of the derivative of the magnetization coexistence diameter near the critical endpoint, in agreement with previous theoretical predictions.

DOI
10.1142/s0129183109014424

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Using the Wang-Landau sampling method with a two-dimensional random walk we determine the density of states for an asymmetric Ising model with two- and three-body interactions on a triangular lattice, in the presence of an external field. With an accurate density of states we were able to map out the phase diagram accurately and perform quantitative finite-size analyses at, and away from, the critical endpoint. We observe a clear divergence of the curvature of the spectator phase boundary and of the magnetization coexistence diameter derivative at the critical endpoint, and the exponents for both divergences agree well with previous theoretical predictions.
We use a two-dimensional Wang-Landau sampling algorithm to calculate the density of states for two discrete spin models and then extract their phase diagrams. The first system is an asymmetric Ising model on a triangular lattice with two- and three-body interactions in an external field. An accurate density of states allows us to locate the critical endpoint accurately in a two-dimensional parameter space. We observe a divergence of the spectator phase boundary and of the temperature derivative of the magnetization coexistence diameter at the critical endpoint in quantitative agreement with theoretical predictions. The second model is a Q-state Potts model in an external field H. We map the phase diagram of this model for Q > 8 and observe a first-order phase transition line that starts at the H = 0 phase transition point and ends at a critical point (Tc,Hc), which must be located in a two-dimensional parameter space. The critical field Hc(Q) is positive and increases with Q, in qualitative agreement with previous theoretical predictions.
Abstract. The critical properties of the randomly site-diluted two-dimensional Ising model were studied using the Wang-Landau algorithm. The concentration of nonmagnetic sites was q = 0.1; the remaining sites were occupied by magnetic particles. The study was carried out in the appro-priate restricted but dominant energy subspaces. The main effort was focused on the specific heat and magnetic susceptibility by using the density of states for the model for lattices with linear size L = 20-120. The finite size scaling behavior of the specific heat and susceptibility was studied. The ratio of the critical exponents (α/ν) is negative (consistent with the Harris criterion), while the ratio (γ/ν) appears to assume its pure Ising model value (weak universality). 1.
Abstract We study the critical properties of the antiferromagnetic spin-1/2 Ising model in an external field on the square lattice. Using tomographic entropic sampling, a flat-histogram simulation method, we estimate the number of configurations, , and related microcanonical averages in the energy-magnetization space, for system sizes L = 10–30. The critical line and exponents are calculated using finite-size scaling analysis in the temperature-external field plane. With these estimates in hand, we perform detailed studies of critical behavior using Metropolis sampling of larger systems ( ). These results are compared to several approximate theoretical methods. Our estimates of critical exponents and Binder’s reduced fourth cumulant along the critical line are in very good agreement with their respective literature values for the two-dimensional Ising universality class. We verify as well that the specific heat scales along the critical line, as expected for an Ising-like critical point.