Limit shape phase transitions: a merger of arctic circles

TL;DR

This paper studies a phase transition in a statistical model where two arctic circles merge, providing insights into a universal third-order transition related to the Gross-Witten-Wadia transition in lattice QCD.

Contribution

It introduces a free fermion model that visualizes the merger of arctic circles as a universal phase transition, connecting it to lattice QCD phenomena.

Findings

The phase transition is a merger of two liquid regions called arctic circles.

The transition corresponds to the Gross-Witten-Wadia transition in lattice QCD.

The transition is universal and persists under certain symmetries and interactions.

Abstract

We consider a free fermion formulation of a statistical model exhibiting a limit shape phenomenon. The model is shown to have a phase transition that can be visualized as the merger of two liquid regions - arctic circles. We show that the merging arctic circles provide a space-time resolved picture of the phase transition in lattice QCD known as Gross-Witten-Wadia transition. The latter is a continuous phase transition of the third order. We argue that this transition is universal and is not spoiled by interactions if parity and time-reversal symmetries are preserved. We refer to this universal transition as the Merger Transition.