Wang-Landau sampling of an asymmetric ising model: a study of the critical endpoint behavior

Abstract

We use the Wang-Landau algorithm to calculate a density of states for 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 determine the phase diagram and to study the critical behavior of this model at and near the critical endpoint. We observe a divergence of the curvature of the spectator phase boundary at the critical endpoint in accordance with theoretical predictions.

Uncovering the secrets of unusual phase diagrams: applications of two-dimensional Wang-Landau sampling

“…(2)). Our tests [45,46] showed that the critical line T c (H) for this asymmetric Ising model is in the same universality class as the two-dimensional Q = 3 Potts model [47], as expected due to symmetry considerations. We recall that the conjectured values [47] for the critical exponents of the 2D Q = 3 Potts model are α = 1/3, β = 1/9, γ = 13/9, and ν = 5/6.…”

“…In particular, for J = 1 and J 3 = 2 (parameters used here) there is a CE that is well-separated from a critical point at the end of the first-order phase transition line. We use Wang-Landau sampling [3][4][5] described in Sec.II with E = ∑ i j S i S j + 2 ∑ i jk S i S j S k and M = ∑ i S i to determine the density of states g(E, M), and from it we obtain thermodynamical quantities such as the magnetization, specific heat, susceptibility, order parameter [45,46], etc. Multiple, independent random walks were performed to look for unexpected behavior resulting from different random number streams as well as to allow the determination of error bars.…”

Critical endpoint behavior: A Wang–Landau study

“…Using data for L = 30, 33, 36, 42 and finite-size scaling relations, the critical endpoint for L = ∞ is estimated as (T , H ) CE = (2.443(10), −2.934 (10)). Our tests [8,9] showed that the critical line T c (H ) is in the same universality class as the two-dimensional Q = 3 Potts model [10], as expected due to symmetry considerations. We recall that the conjectured values [10] for the critical exponents of the 2D Q = 3 Potts model are α = 1/3, β = 1/9, γ = 13/9, and ν = 5/6.…”

“…We use with random walks in the two-dimensional parameter space (E, M), where E = − ij S i S j − 2 ij k S i S j S k and M = i S i , to determine the density of states g(E, M), and from it we obtain thermodynamical quantities such as the magnetization, specific heat, susceptibility, order parameter [8,9], etc. We start the simulation with a random spin configuration and, because the density of states is unknown, we simply set g(E, M) = 1 for all possible (E, M).…”

Estudo dos potenciais termodinâmico na coexistência de fase em modelos de rede através de simulação de Monte Carlo

“…Para explorar a região entre as fases, é necessária a utilização de outros métodos de simulação de Monte Carlo. Existem alguns métodos, conhecidos como métodos de histograma uniforme, que permitem acessar a região não alcançada pelo algoritmo de Metropolis, tais como o método de Wang-Landau [16][17][18] e o Método Multicanônico [19,20]. O método Wang-Landau permite um passeio aleatório no parâmetro de interesse (energia, volume ou número de partículas).…”