Hybrid Monte Carlo algorithm for studying the Edwards-Anderson model

The complexity of the study of spin glasses is related to their frustrations, due to which classical Monte Carlo algorithms experience serious difficulties when trying to calculate such systems. The main object of research in this paper is two-dimensional Edwards–Anderson model on a square lattice. In the paper, we propose an optimized Hybrid Monte Carlo method for calculating the values of thermodynamic averages and ground state energies of the frustrated spin glass model. The validity of the results is confirmed by comparison with numerical simulation with the parallel tempering Monte Carlo method, complete enumeration algorithm and robust machine learning approach – RBM neural network. The proposed algorithm has a number of advantages: possible high parallelization of the algorithm to speed up simulation, calculation accuracy and low resource consumption, which allows to calculate lattices of relatively large size. This algorithm can be applied to calculations of lattices with different geometry and sizes.