Refined functional relations for the elliptic SOS model

R. J. Baxter

Jules Lamers

In this paper we extend previous work of Galleas and the author to elliptic sos models. We demonstrate that the dynamical reflection algebra can be exploited to obtain a functional equation characterizing the partition function of an elliptic sos model with domain-wall boundaries and one reflecting end. Special attention is paid to the structure of the functional equation. Through this approach we find a novel multiple-integral formula for that partition function.

Schorr, Anke

This work deals on the one hand with how to use the representation theory of a quantum group ( [14]) to investigate a statistical mechanical model and on the other hand with how to solve the statistical mechanical model by Sklyanin's method of separation of variables.[47].More concretely, we use the elliptic quantum group E y,'I)(sl2) established by Felder in [29, 25] to investigate the SOS eight-vertex model established by Date, Jimbo, Miwa and Okado [10] with antiperiodic boundary conditions which are the reason that Bethe ansatz fails and we have to use Sklyanin's method of separation of variables [47].The SOS eight-vertex model is a face-model version of Baxter's original eight-vertex model [3].It is related to the elliptic quantum group E y,'I)(sl2), since we rediscover its Boltzmann weights We(c, b, a, dlz) by a suitably discretized version of the R-matrix Re(z,.\)defining E Y,'I)(sl2)' This relation reads

Evgueni K. Sklyanin, Takashi Takebe

Markus Arndt

Ghali Filali