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

Area of Science:

• Computational physics
• Statistical mechanics

Background:

• Calculating absolute free energy in spin lattice models is computationally demanding.
• Existing methods like population annealing Monte Carlo (PAMC) are effective but can be complex.

Purpose of the Study:

• To present an efficient and simple method for measuring absolute free energy in spin lattice models.
• To compare the performance of the proposed method against population annealing Monte Carlo.

Main Methods:

• Utilized a two-stage parallel tempering Monte Carlo (PTMC) combined with the free energy perturbation method.
• Employed the three-dimensional Edwards-Anderson Ising spin glass model for benchmark testing.
• Compared results with population annealing Monte Carlo (PAMC).

Main Results:

• The proposed PTMC approach requires minimal modifications to standard PTMC codes and has little overhead.
• PTMC achieved comparable efficiency in measuring absolute free energy to PAMC, despite using fewer temperatures.
• Simulating each temperature for longer durations in PTMC contributed to its efficiency.

Conclusions:

• The two-stage parallel tempering Monte Carlo method offers an efficient and accessible alternative for absolute free energy calculations.
• This method provides a viable and less complex approach for studying spin lattice models.
• The findings suggest that optimizing simulation time per temperature can be as effective as increasing the number of temperatures.