Wednesday, October 19, 2022 3:00 PM
Zhenyuan Zhang

Abstract: We discuss the existence and uniqueness (in terms of different boundary conditions) of the infinite-volume Gibbs measure for the Ising model on the integer lattice. The key tool for proving the existence is the FKG inequality. A phase transition arises between the uniqueness and non-uniqueness of the infinite-volume Gibbs measure. We show that non-uniqueness occurs when the temperature is low enough in dimension two, using the Peierls argument.