Torpid Mixing of Simulated Tempering on the Potts Model by Bhatnagar and Randall

I. Abstract and Intro The purpose of this paper is two fold. First, it proves that temperature-based sampling algorithms (specifically simulated tempering and swapping), which have successfully been used to sample bimodal distributions such as the low-temperature mean-field Ising model, can fail to converge rapidly on the more general Potts model. This is due to the nature of the phase change with three states or greater. Secondly, it presents a variant of the swapping algorithm, the Flat-Swap algorithm, and proves that it is rapidly mixing for any bimodal mean-field model.