Thermodynamics of the six-vertex model in an L-shaped domain

TL;DR

This paper analyzes the thermodynamic behavior of the six-vertex model in an L-shaped domain, revealing a third-order phase transition and providing explicit free energy calculations using Coulomb gas methods.

Contribution

It introduces a Coulomb gas approach to study the six-vertex model in an L-shaped domain, deriving the free energy and phase transition characteristics.

Findings

Identifies a third-order phase transition in the model.

Derives explicit free energy as a function of domain parameters.

Connects results to dimer models and perfect matchings.

Abstract

We consider the six-vertex model in an L-shaped domain of the square lattice, with domain wall boundary conditions. For free-fermion vertex weights the partition function can be expressed in terms of some Hankel determinant, or equivalently as a Coulomb gas with discrete measure and a non-polynomial potential with two hard walls. We use Coulomb gas methods to study the partition function in the thermodynamic limit. We obtain the free energy of the six-vertex model as a function of the parameters describing the geometry of the scaled L-shaped domain. Under variations of these parameters the system undergoes a third-order phase transition. The result can also be considered in the context of dimer models, for the perfect matchings of the Aztec diamond graph with a cut-off corner.