This article is cited in 3 papers

The symmetry of the partition function of some square ice models

J.-Ch. Aval

Laboratoire Bordelais de Recherche en Informatique, Université Bordeaux 1, CNRS, Talence, France

Abstract: We consider the partition function $Z(N;x_1,\dots,x_N,y_1,\dots,y_N)$ of the square ice model with domain wall boundary conditions. We give a simple proof that $Z$ is symmetric with respect to all its variables when the global parameter $a$ of the model is set to the special value $a=e^{i\pi/3}$. Our proof does not use any determinant interpretation of $Z$ and can be adapted to other situations (e.g., to some symmetric ice models).

Keywords: alternating-sign matrix, square ice model, partition function, Yang–Baxter equation.

Received: 27.03.2009
Revised: 12.05.2009

DOI: 10.4213/tmf6442

 English version: Theoretical and Mathematical Physics, 2009, 161:3, 1582–1589

Bibliographic databases:

• 
• 
• 
• 
•