# Construction for Ergodic Gibbs measure and Classification of Phases

In this talk, I will introduce Ergodic Gibbs Measures (EGM) for infinite periodic bipartite graphs and the definition of phases based on height fluctuations wrt this measure. I will present a sketch of how to construct EGMs with fixed slopes as well as how phase classifications can be done using information about the amoeba of characteristic functions of the graph. I will illustrate the theory using honeycomb dimers.

**Date published:**Wednesday, December 7, 2022