Distribution of metastable states of spin glasses

Abstract

The complex behavior of systems like spin glasses, proteins or neural networks is typically explained in terms of a rugged energy or fitness landscape. Within the high-dimensional conformation space of these systems one finds features like barriers, saddle points, and metastable states whose number - at least in the case of spin glasses - grows exponentially with the size of the system. We propose a novel Monte Carlo sampling algorithm that employs an ensemble of short Markovian chains in order to visit all metastable states with equal probability. We apply this algorithm in order to measure the number of metastable states for the two-dimensional and the three-dimensional Edwards-Anderson model and compare with theoretical predictions.