Colloquium- Alexander Abanov (Stony Brook University)- Limit Shape Phase Transitions

Abstract: A limit shape phenomenon in statistical mechanics is the appearance of a most probable macroscopic state. This state is usually characterized by a well-defined boundary separating frozen and liquid spatial regions. We will review a few examples of the models leading to the appearance of limit shapes. Then we consider a class of topological phase transitions in the limit shape problem of statistical mechanics. The problem considered is generally known as the Arctic circle problem. One can visualize the considered transition as merging two melted regions (Arctic circles). We establish the mapping, which identifies the transition as the Gross-Witten-Wadia transition known in lattice QCD and random matrix problems. It is a continuous phase transition of the third order. We identify universal features of the limiting shape close to the transition using the free fermion and hydrodynamic description.