Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physics Procedia

Wang-Landau Algorithm in a Two-Dimensional Spin–1 Blume-Capel Model

Wooseop Kwak

Published Jan 1, 2012• 1 citation
Publisher

Abstract

We study spin−1 Blume-Capel (BC) model in two-dimensions in terms of the Wang-Landau (WL) algorithm, which is one of typical entropic sampling methods with lots of applications in statistical physics and biophysics. The WL algorithm lets us estimate the joint density of states as a function of energy and the order parameter in the BC model.

DOI
10.1016/j.phpro.2012.05.013

Related papers

An efficient determination of the critical temperature of the Blume-Capel model

Seol Ryu, Wooseop Kwak

We determinte the critical temperature of the spin-1 Blume-Capel (BC) model by using the derivative of the free energy with respect to the crystal field and call this quantity the “ preference ” parameter. We carry out simulations of the BC model on a two-dimensional square lattice by using the Wang-Landau sampling method. We measure the susceptibility and the critical temperature of the BC model by using the preference parameter and compare them with those obtained by using the magnetization. We find that the preference parameter works well for the BC model and improves the simulation performance.

Journal of the Korean Physical Society•Mar 1, 2013•5 citations

Multiphase structure of finite‐temperature phase diagram of the Blume–Capel model. Wang–Landau sampling method

Grzegorz Pawłowski

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)

arXiv:cond-mat/0703299•physica status solidi (b)•Dec 1, 2005•8 citations

First-order phase transition and tricritical scaling behavior of the Blume-Capel model: A Wang-Landau sampling approach

Wooseop Kwak, Joo-Hyeok Jeong, Juhee Lee +1 more

We investigate the tricritical scaling behavior of the two-dimensional spin-1 Blume-Capel model by using the Wang-Landau method of measuring the joint density of states for lattice sizes up to 48×48 sites. We find that the specific heat deep in the first-order area of the phase diagram exhibits a double-peak structure of the Schottky-like anomaly appearing with the transition peak. The first-order transition curve is systematically determined by employing the method of field mixing in conjunction with finite-size scaling, showing a significant deviation from the previous data points. At the tricritical point, we characterize the tricritical exponents through finite-size-scaling analysis including the phenomenological finite-size scaling with thermodynamic variables. Our estimation of the tricritical eigenvalue exponents, yt=1.804(5), yg=0.80(1), and yh=1.925(3), provides the first Wang-Landau verification of the conjectured exact values, demonstrating the effectiveness of the density-of-states-based approach in finite-size scaling study of multicritical phenomena.

arXiv:1504.02565•Physical Review E•Aug 24, 2015•66 citations

The parallel Wang-Landau algorithm for joint density of states calculation

V. I. Egorov, Olga G. Maksimova, A R Baidganov

The Wang-Landau algorithm is used for estimating density of states. The joint density of states (JDOS) with two parameters gives more information than conventional one but it requires a huge computational time. Recently, the developing of fast algorithms for the JDOS calculation is an actual problem. In this work, we employ the modified parallel WL algorithm for JDOS, which combines ideas of global updates and two level methods. This algorithm is checked the three-dimensional Ising and Potts models. The method of obtaining phase diagrams from JDOS is demonstrated for Ising model.

Journal of Physics Conference Series•Dec 1, 2018•2 citations

Wang–Landau study of the 2d random-bond Blume–Capel model

Anastasios Malakis, A. Nihat Berker, Ioannis A. Hadjiagapiou +1 more

We study, via a two-stage Wang–Landau (WL) strategy, the random-bond version of the square lattice ferromagnetic Blume–Capel (BC) model, in both the first- and second-order phase transition regimes of the pure model. The second-order phase transition, emerging under random bonds from the second-order regime of the pure model, has the same values of critical exponents as the 2d Ising universality class, with the effect of the bond disorder on the specific heat being well described by double-logarithmic corrections. On the other hand, the second-order transition, emerging under bond randomness from the first-order regime of the pure model, has a distinctive universality class with v=1.30(6) and β/v=0.128(5). These results amount to a strong violation of universality principle of critical phenomena, since these two second-order transitions, with different sets of critical exponents, are between the same ferromagnetic and paramagnetic phases. Furthermore, the latter of these two sets of results supports an extensive but weak universality, since it has the same magnetic critical exponent (but a different thermal critical exponent) as a wide variety of 2d systems with and without quenched disorder.

Physics Procedia•Feb 1, 2010•0 citations

Study of the Antiferromagnetic Blume-Capel Model on kagomé Lattice

Chi‐Ok Hwang, Sojeong Park, Wooseop Kwak

We study the anti-ferromagnetic (AF) Ising model and the AF Blume-Capel (BC) model on the kagomé lattice. Using the Wang-Landau sampling method, we estimate the joint density functions for both models on the lattice, and we obtain the exact critical magnetic fields at zero temperature by using the micro-canonical analysis. We also show the patterns of critical lines for the models from micro-canonical analysis.

Journal of Physics Conference Series•Sep 1, 2016•2 citations
We study spin−1 Blume-Capel (BC) model in two-dimensions in terms of the Wang-Landau (WL) algorithm, which is one of typical entropic sampling methods with lots of applications in statistical physics and biophysics. The WL algorithm lets us estimate the joint density of states as a function of energy and the order parameter in the BC model.
We determinte the critical temperature of the spin-1 Blume-Capel (BC) model by using the derivative of the free energy with respect to the crystal field and call this quantity the “ preference ” parameter. We carry out simulations of the BC model on a two-dimensional square lattice by using the Wang-Landau sampling method. We measure the susceptibility and the critical temperature of the BC model by using the preference parameter and compare them with those obtained by using the magnetization. We find that the preference parameter works well for the BC model and improves the simulation performance.
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 investigate the tricritical scaling behavior of the two-dimensional spin-1 Blume-Capel model by using the Wang-Landau method of measuring the joint density of states for lattice sizes up to 48×48 sites. We find that the specific heat deep in the first-order area of the phase diagram exhibits a double-peak structure of the Schottky-like anomaly appearing with the transition peak. The first-order transition curve is systematically determined by employing the method of field mixing in conjunction with finite-size scaling, showing a significant deviation from the previous data points. At the tricritical point, we characterize the tricritical exponents through finite-size-scaling analysis including the phenomenological finite-size scaling with thermodynamic variables. Our estimation of the tricritical eigenvalue exponents, yt=1.804(5), yg=0.80(1), and yh=1.925(3), provides the first Wang-Landau verification of the conjectured exact values, demonstrating the effectiveness of the density-of-states-based approach in finite-size scaling study of multicritical phenomena.
The Wang-Landau algorithm is used for estimating density of states. The joint density of states (JDOS) with two parameters gives more information than conventional one but it requires a huge computational time. Recently, the developing of fast algorithms for the JDOS calculation is an actual problem. In this work, we employ the modified parallel WL algorithm for JDOS, which combines ideas of global updates and two level methods. This algorithm is checked the three-dimensional Ising and Potts models. The method of obtaining phase diagrams from JDOS is demonstrated for Ising model.
We study, via a two-stage Wang–Landau (WL) strategy, the random-bond version of the square lattice ferromagnetic Blume–Capel (BC) model, in both the first- and second-order phase transition regimes of the pure model. The second-order phase transition, emerging under random bonds from the second-order regime of the pure model, has the same values of critical exponents as the 2d Ising universality class, with the effect of the bond disorder on the specific heat being well described by double-logarithmic corrections. On the other hand, the second-order transition, emerging under bond randomness from the first-order regime of the pure model, has a distinctive universality class with v=1.30(6) and β/v=0.128(5). These results amount to a strong violation of universality principle of critical phenomena, since these two second-order transitions, with different sets of critical exponents, are between the same ferromagnetic and paramagnetic phases. Furthermore, the latter of these two sets of results supports an extensive but weak universality, since it has the same magnetic critical exponent (but a different thermal critical exponent) as a wide variety of 2d systems with and without quenched disorder.