Lattice Systems

Lattice systems form a widely studied class of models originating in statistical mechanics, and consisting of single-site observables (functions or operators) describing "spins," living on infinite lattices. They have found applications in various other fields, in physics (e.g., field theory), mathematics (dynamical systems and probability theory), and also as models for epidemics and populations. Their major interest and difference with other stochastic processes is due to the occurrence of various phase transitions, where the dependence on parameters becomes nonsmooth, and/or the number of measures associated with a certain parameter can change.