Acceleration of convergence to the thermodynamic equilibrium by introducing shuffling operations to the Metropolis algorithm of Monte Carlo simulations

This paper introduces a broad class of operations, called "shuffling trials", used to design nonphysical pathways. It is shown that in general the equilibrium distribution of a system can be attained when physically possible pathways are interrupted regularly by nonphysical shuffling trials. Including properly chosen shuffling trials in the commonly applied Metropolis algorithm often considerably accelerates the convergence to the equilibrium distribution. Shuffling trials are usually global changes in the system, sampling efficiently every set of the metastable configurations of the system. Shuffling trials are generated by symmetric stochastic matrices. Since ergodicity is not a required property, it is particularly easy to construct these matrices in accordance with the specificity of the system. The design, application, and efficiency of the shuffling trials in Monte Carlo simulations are demonstrated on an Ising model of two-dimensional spin lattices.