Entropic algorithms and the lid method as exploration tools for complex landscapes

TL;DR

This paper combines the lid algorithm with entropic Monte Carlo methods to explore complex energy landscapes, revealing distinct local density of states in Edwards-Anderson models across dimensions.

Contribution

It introduces an improved landscape exploration method by integrating the lid algorithm with entropic sampling techniques for complex systems.

Findings

Local density of states is nearly flat in 2D Edwards-Anderson model.

Local density of states is nearly exponential in 3D Edwards-Anderson model.

Lid dependence analysis helps estimate the global density of states.

Abstract

Monte Carlo algorithms such as the Wang-Landau algorithm and similar `entropic' methods are able to accurately sample the density of states of model systems and thereby give access to thermal equilibrium properties at any temperature. Thermal equilibrium is however not achievable at low temperatures in glassy systems. Such systems are characterized by a multitude of metastable configurations, pictorially referred to as `valleys' of an energy landscape. Geometrical properties of the landscape, e.g. the local density of states describing the distribution in energy of the states belonging to a single valley, are key to understand the dynamical properties of such systems. In this paper we combine the lid algorithm, a tool for landscape exploration previously applied to a range of models, with the Wang-Swendsen algorithm. To test this improved exploration tool, we consider a paradigmatic complex system, the Edwards-Andersom model in two and three spatial dimension. We find a striking difference between the energy dependence of the local density of states in the two cases: nearly flat in the first case, and nearly exponential in the second. The lid dependence of the data is analyzed to estimate the form of the global density of states.