Efficiently Estimating the Density of States of Frustrated Systems

Frustrated spin systems are known to stymie entropic samplers -- algorithms designed to statistically estimate the density of states at different energy intervals of physical systems. Intricate or rugged energy landscapes often cause these to yield false convergences to erroneous density estimations. Here, we report on the performance of a population annealing based algorithm on Ising spin glasses demonstrating orders of magnitude scaling advantages over exiting state-of-the-art algorithms. To demonstrate the algorithm's advantages in a verifiable manner, we introduce a scheme that allows us to achieve an exact count of the degeneracies of the ground- and first-excited states of the tested instances. We discuss the practical implications of having a fast algorithm for the calculation of the density of states of frustrated systems.