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

## TL;DR

This paper introduces a generalized, macroscopically constrained Wang-Landau method for efficiently computing the density of states in systems with multiple order parameters, enabling rapid phase diagram analysis.

## Contribution

It develops a novel approach that decomposes multidimensional random walks into constrained one-dimensional walks, facilitating quick thermodynamic calculations across phase diagrams.

## Key findings

- Successfully applied to a spin-crossover model with complex interactions.
- Enabled rapid computation of phase diagrams and order-parameter distributions.
- Demonstrated efficiency in systems with multiple macroscopic parameters.

## 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.