Construction of an irreducible Markov chain in the Ising model

In applied mathematics, construction of an irreducible Markov Chain in the Ising model is the first step in overcoming a computational obstruction encountered when a Markov chain Monte Carlo method is used to get an exact goodness-of-fit test for the finite Ising model.

The Ising model was used to study magnetic phase transitions at the very beginning, and now it is one of the most famous models of interacting systems.