Binary tree summation Monte Carlo simulation for Potts models

In this talk, we briefly comment on Sweeny and Gliozzi methods, cluster Monte Carlo method, and recent transition matrix Monte Carlo for Potts models. We mostly concentrate on a new algorithm known as "binary tree summation". Some of the most interesting features of this method will be highlighted - such as simulating fractional number of Potts states, as well as offering the partition function and thermodynamic quantities as functions of temperature in a single run.