On the symmetry of the partition function of some square ice models

TL;DR

This paper proves the symmetry of the partition function in certain square ice models at a specific parameter value, using a novel approach that avoids determinantal methods and can be applied to other models.

Contribution

It provides a simple, adaptable proof of the partition function's symmetry for square ice models at a special parameter value, bypassing traditional determinantal techniques.

Findings

Partition function Z is symmetric in all variables at a=exp(iπ/3)

Proof does not rely on determinantal interpretation

Method can be adapted to other symmetric ice models

Abstract

We consider the partition function Z(N;x_1,...,x_N,y_1,...,y_N) of the square ice model with domain wall boundary. We give a simple proof of the symmetry of Z with respect to all its variables when the global parameter a of the model is set to the special value a=exp(i\pi/3). Our proof does not use any determinantal interpretation of Z and can be adapted to other situations (for examples to some symmetric ice models).