Exact sampling from nonattractive distributions using summary states - art. no. 036113

Propp and Wilson's method of coupling from the past allows one to efficient ly generate exact samples from attractive statistical distributions (e.g., the ferromagnetic Ising model). This method may be generalized to nonattrac tive distributions by the use of summary states, as first described by Hube r. Using this method, we present exact samples from a frustrated antiferrom agnetic triangular Ising model and the antiferromagnetic q=3 Potts model. W e discuss the advantages and limitations of the method of summary states fo r practical sampling, paying particular attention to the slowing down of th e algorithm at low temperature. In particular, we show that such slowing do wn can occur in the absence of a physical phase transition.