Measuring free energy in spin-lattice models using parallel tempering Monte Carlo.

Abstract

An efficient and simple approach of measuring the absolute free energy as a function of temperature for spin lattice models using a two-stage parallel tempering Monte Carlo and the free energy perturbation method is discussed and the results are compared with those of population annealing Monte Carlo using the three-dimensional Edwards-Anderson Ising spin glass model as benchmark tests. This approach requires little modification of regular parallel tempering Monte Carlo codes with also little overhead. Numerical results show that parallel tempering, even though using a much less number of temperatures than population annealing, can nevertheless equally efficiently measure the absolute free energy by simulating each temperature for longer times.