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Seminar

Ising Model II

Speaker
Zhenyuan Zhang
Date
Wed, Oct 19 2022, 3:00pm
Location
383N

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.