# Density of states for systems with multiple order parameters: a constrained Wang-Landau method

## TL;DR

This paper introduces a constrained Wang-Landau Monte Carlo method to efficiently compute the joint density of states for systems with multiple order parameters, demonstrated on a complex spin model with long-range interactions.

## Contribution

The paper presents a novel constrained Wang-Landau approach enabling calculation of joint density of states for systems with multiple order parameters, including transformations for different external conditions.

## Key findings

- Successfully calculated joint DOS for a complex spin system.
- Demonstrated the method's applicability to various parameter sets.
- Provided insights into the system's thermodynamic behavior.

## Abstract

A macroscopically constrained Wang-Landau Monte Carlo method was recently proposed to calculate the joint density of states (DOS) for systems with multiple order parameters. Here we demonstrate results for a nearest-neighbor Ising antiferromagnet with ferromagnetic long-range interactions (a model spin-crossover material). Its two relevant order parameters are the magnetization $M$ and the staggered magnetization $M_{\rm s}$. The joint DOS, $g(E,M,M_{\rm s})$ where $E$ is the total system energy, is calculated for zero external field and long-range interaction strength, and then obtained for arbitrary values of these two field-like model parameters by a simple transformation of $E$. Illustrations are shown for several parameter sets.