Intermediate model between Majority voter PCA and its Mean Field model

Abstract: Probabilistic Cellular Automata (PCA) are simple models used to study dynamical phase transitions. There exist mean field approximations to PCA that can be shown to exhibit a phase transition. We introduce a model interpolating between a class of PCA, called majority voters, and their corresponding mean field models. Using graphical methods, we prove that this model undergoes a phase transition.