In this paper we consider the Gibbs sampler dynamics with simulated annealing and partially parallel updating scheme, as proposed by Trouve. It is known that in some cases the support of the limiting measure does not coincide with the set of global maxima of the underlying energy function. We provide some new simple examples of this undesirable behavior. However, we also prove that for one-dimensional binary models with nearest neighbor interaction the algorithm works "generically." We prove also that for two-dimensional models with nearest neighbor ferromagnetic constant interactions the algorithm works.
"Convergence of Some Partially Parallel Gibbs Samplers with Annealing." Ann. Appl. Probab. 3 (1) 137 - 153, February, 1993. https://doi.org/10.1214/aoap/1177005511