Comparing Monte Carlo methods for finding ground states of Ising spin glasses: population annealing, simulated annealing and parallel tempering

TL;DR

This paper compares population annealing, simulated annealing, and parallel tempering Monte Carlo methods for finding ground states in 3D Ising spin glasses, highlighting population annealing's efficiency and effectiveness.

Contribution

It introduces and evaluates population annealing Monte Carlo as a new heuristic for solving spin-glass ground states, comparing its performance to established methods.

Findings

Population annealing is more efficient than simulated annealing.

Population annealing performs comparably to parallel tempering.

All methods effectively find ground states in 3D Ising spin glasses.

Abstract

Population annealing is a Monte Carlo algorithm that marries features from simulated annealing and parallel tempering Monte Carlo. As such, it is ideal to overcome large energy barriers in the free-energy landscape while minimizing a Hamiltonian. Thus, population annealing Monte Carlo can be used as a heuristic to solve combinatorial optimization problems. We illustrate the capabilities of population annealing Monte Carlo by computing ground states of the three-dimensional Ising spin glass with Gaussian disorder, whilst comparing to simulated annealing and parallel tempering Monte Carlo. Our results suggest that population annealing Monte Carlo is significantly more efficient than simulated annealing but comparable to parallel tempering Monte Carlo for finding spin-glass ground states.