Density of States for a Specified Correlation Function and the Energy Landscape

TL;DR

This paper introduces a Monte Carlo method to analyze the density of states and energy landscape roughness of disordered microstructures with specified correlation functions, linking structural degeneracy to energy landscape features.

Contribution

It presents the first direct calculation of the density of states for microstructures based on correlation functions using a novel Monte Carlo approach.

Findings

Density of states can be quantified via Monte Carlo simulations.

Energy landscape roughness correlates with structural degeneracy.

The method is validated across various disordered systems.

Abstract

The degeneracy of two-phase disordered microstructures consistent with a specified correlation function is analyzed by mapping it to a ground-state degeneracy. We determine for the first time the associated density of states via a Monte Carlo algorithm. Our results are described in terms of the roughness of the energy landscape, defined on a hypercubic configuration space. The use of a Hamming distance in this space enables us to define a roughness metric, which is calculated from the correlation function alone and related quantitatively to the structural degeneracy. This relation is validated for a wide variety of disordered systems.