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arXiv · 0903.0777

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

Jean-Christophe Aval
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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(iπ/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).

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Jean-Christophe Aval. 2009-03-04. On the symmetry of the partition function of some square ice models. https://doi.org/10.1007/s11232-009-0146-8

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