Boltzmann weights and fusion procedure for the rational seven-vertex SOS model

TL;DR

This paper constructs and analyzes integrable 7-vertex and SOS models, deriving Boltzmann weights via hypergeometric series, and introduces a new family of vertex models including the 11-vertex model with a vertex-SOS correspondence.

Contribution

It develops a fusion-based method to construct generalized integrable models and explicitly computes Boltzmann weights using hypergeometric series, establishing a vertex-SOS correspondence.

Findings

Boltzmann weights expressed as terminating hypergeometric series ${}_{9}F_8$

Constructed a new family of vertex models including the 11-vertex model

Established vertex-SOS correspondence with spectral parameter independence

Abstract

We consider seven-vertex two-dimensional integrable statistical model. With the help of intertwining vector method we construct its counterpart integrable model of SOS type. More general models of both types are constructed by means of fusion procedure. For SOS models we calculate the Boltzmann weights in terms of terminating hypergeometric series ${}_{9} F_8.$ Then using the similarity transformation for $R$-operators we construct a new family of vertex models containing the 11-vertex model as the simplest representative. For this new set of models the vertex-SOS correspondence is constructed: we find the intertwining vectors, show that they do not depend on spectral parameter and the SOS statistical weights are similar to those obtained from the 7-vertex model.