Macroscopically constrained Wang-Landau method for systems with multiple order parameters and its application to drawing complex phase diagrams

Abstract

A generalized approach to Wang-Landau simulations, macroscopically constrained Wang-Landau, is proposed to simulate the density of states of a system with multiple macroscopic order parameters. The method breaks a multidimensional random-walk process in phase space into many separate, one-dimensional random-walk processes in well-defined subspaces. Each of these random walks is constrained to a different set of values of the macroscopic order parameters. When the multi-variable density of states is obtained for one set of values of field-like model parameters, the density of states for any other values of these parameters can be obtained by a simple transformation of the total system energy. All thermodynamic quantities of the system can then be rapidly calculated at any point in the phase diagram. We demonstrate how to use the multi-variable density of states to draw the phase diagram, as well as order-parameter probability distributions at specific phase points, for a model spin-crossover material: an antiferromagnetic Ising model with ferromagnetic long-range interactions. The field-like parameters in this model are an effective magnetic field and the strength of the long-range interaction.

35 pages, 11 figures

References in corpus (13)

• Wang-Landau Algorithm: a Theoretical Analysis of the Saturation of the Error
• Realization of the mean-field universality class in spin-crossover materials
• Scalable replica-exchange framework for Wang-Landau sampling
• Analysis of the convergence of the 1/t and Wang-Landau algorithms in the calculation of multidimensional integrals
• Generic folding and transition hierarchies for surface adsorption of hydrophobic-polar lattice model proteins
• Improving Wang-Landau sampling with adaptive windows
• Monte Carlo Simulations of the Critical Properties of a Ziff-Gulari-Barshad model of Catalytic CO Oxidation with Long-range Reactivity
• From Network Reliability to the Ising Model: A Parallel Scheme for Estimating the Joint Density of States
• Intrinsic convergence properties of entropic sampling algorithms
• Phase diagrams and free-energy landscapes for model spin-crossover materials with antiferromagnetic-like nearest-neighbor and ferromagnetic-like long-range interactions
• Monte Carlo Studies of the Ising Antiferromagnet with a Ferromagnetic Mean-field Term
• Density of states for systems with multiple order parameters: a constrained Wang-Landau method
• Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based models

Cited by in corpus (7)

• Logarithmic finite-size scaling correction to the leading Fisher zeros in the p-state clock model: A higher-order tensor renormalization group study
• Nontrivial phase diagram for an elastic interaction model of spin crossover materials with antiferromagnetic-like short-range interactions
• Partition function zeros of the p-state clock model in the complex temperature plane
• Multistability in an unusual phase diagram induced by the competition between antiferromagnetic-like short-range and ferromagnetic-like long-range interactions
• Phase diagrams and free-energy landscapes for model spin-crossover materials with antiferromagnetic-like nearest-neighbor and ferromagnetic-like long-range interactions
• Density of states for systems with multiple order parameters: a constrained Wang-Landau method
• Efficient implementation of the Wang-Landau algorithm for systems with length-scalable potential energy functions