Integrating cluster algorithms and transition matrix methods

The transition matrix procedure accumulates in a single matrix all accepted and rejected transitions generated during biased sampling of statistical systems, increasing the accuracy of calculations of the density of states relative to standard methods that ignore rejected transitions. However, the efficiency of the transition matrix algorithm is limited by the requirement that the system realizations adequately sample the entire physically accessible configuration space. In the Ising model, the slow diffusion of the single spin-flip procedure through this space severely limits the computation speed, especially for large systems.

This talk introduces a more efficient sampling procedure that combines the Wolff and Metropolis algorithms. [1] In particular, the Metropolis acceptance rule is employed at temperatures that slowly increase (or decrease) as the calculation proceeds. Near the critical temperature, however, one or more Wolff cluster flips are periodically performed before reverting to the single spin-flips that are required to populate the transition matrix. Potential methods for extending this strategy to more complicated systems are then proposed.

[1] D. Yevick and Y.H. Lee, Transition Matrix Cluster Algorithms, arXiv:1803.10907