The aim of this paper is to collect definitions and results on the main classes of 2D languages introduced with the attempt of generalizing regular and context-free string languages and in same time preserving some of their nice properties. Almost all the models here described are based on tiles. So we also summarize some results on Wang tiles and its applications.

The Swendsen–Wang algorithm is a sophisticated, widely-used Markov chain for sampling from the Gibbs distribution ferromagnetic Ising and Potts models. This has proved difficult to analyze, due in part its global nature. We present optimal bounds on convergence rate of complete d $$ -ary tree. Our extend non-uniqueness region apply all boundary conditions. show that spatial mixing conditions kn...