# An Efficient Simulation Protocol for Determining the Density of States: Combination of Replica-Exchange Wang-Landau Method and Multicanonical Replica-Exchange Method

## TL;DR

This paper introduces a new simulation protocol combining two advanced algorithms to accurately determine the density of states, demonstrated on the Ising model, outperforming individual methods in precision.

## Contribution

The paper presents the REWL-MUCAREM protocol, integrating REWL and MUCAREM for improved density of states estimation in statistical models.

## Key findings

- REWL-MUCAREM yields more accurate density of states than individual methods.
- The combined protocol outperforms separate REWL and MUCAREM in simulations.
- Validation performed on the square-lattice Ising model.

## Abstract

By combining two generalized-ensemble algorithms, Replica-Exchange Wang-Landau (REWL) method and Multicanonical Replica-Exchange Method (MUCAREM), we propose an effective simulation protocol to determine the density of states with high accuracy. The new protocol is referred to as REWL-MUCAREM, and REWL is first performed and then MUCAREM is performed next. In order to verify the effectiveness of our protocol, we performed simulations of a square-lattice Ising model by the three methods, namely, REWL, MUCAREM, and REWL-MUCAREM. The results showed that the density of states obtained by the REWL-MUCAREM is more accurate than that is estimated by the two methods separately.