A Modified Histogram Method for Disordered Lattices

TL;DR

This paper introduces a modified histogram method that effectively combines data from various disordered lattice configurations, enhancing analysis of disordered systems like relaxor ferroelectric materials.

Contribution

A novel histogram-based approach that extends existing methods to handle multiple disordered lattice configurations simultaneously.

Findings

Successfully applied to a model of relaxor ferroelectric perovskite.

Improves data integration from diverse disordered lattice simulations.

Enhances analysis of disordered materials in computational physics.

Abstract

A new method is developed to extend the histogram method to lattices with any type of disorder. The Monte Carlo single- and multiple-histogram methods were developed to get the most out of only a few simulations, but are restricted to simulations with identical lattice configurations. The method introduced here expands on the histogram method to allow data from various disordered lattice configurations to be optimally combined in a single weighted average result. This method is applied to a simple Ising-like model of the relaxor ferroelectric perovskite solid solution $BaTiO_3$ - $Bi(Zn_{1/2}Ti_{1/2})O_3$ (BT-BZT), in which disorder plays a pivotal role.