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

Jean-Christophe Aval (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique

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).

Mots clés: square ice models; partition functions; Yang-Baxter equation

Domaines: Combinatoire [math.CO]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Jean-Christophe Aval. On the symmetry of the partition function of some square ice models. Theoretical and Mathematical Physics, 2009, 161 (3), pp.1582-1589. ⟨hal-00365802⟩