Random Walk over Basins of Attraction to Construct Ising Energy Landscapes

TL;DR

This paper introduces a novel algorithm that uses random walks over basins of attraction to efficiently construct Ising energy landscapes, revealing detailed features of complex systems like spin glasses.

Contribution

It presents an efficient method for mapping energy landscapes by detecting minima, barriers, and averages, applicable to large and complex systems such as SK spin glasses.

Findings

Successfully applied to SK spin glass Hamiltonian

Predictions align with theoretical approximations

Reveals detailed free energy landscape features

Abstract

An efficient algorithm is developed to construct disconnectivity graphs by a random walk over basins of attraction. This algorithm can detect a large number of local minima, find energy barriers between them, and estimate local thermal averages over each basin of attraction. It is applied to the SK spin glass Hamiltonian where existing methods have difficulties even for a moderate number of spins. Finite-size results are used to make predictions in the thermodynamic limit that match theoretical approximations and recent findings on the free energy landscapes of SK spin glasses.