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Journal of Physics A Mathematical and General

General solution of reflection equation for eight-vertex SOS model

Heng Fan, Bo-Yu Hou, Kangjie Shi

Published Sep 7, 1995• 23 citations
Publisher

Abstract

By using the general solution of the reflection equation for the eight-vertex model, a general solution of the reflection equation for the eight-vertex SOS model is obtained. We also discuss the solution of the reflection equation for the case of the RSOS model.
DOI
10.1088/0305-4470/28/17/010

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In this paper we compute the most general non-diagonal reflection matrices of the RSOS/SOS models and the hard hexagon model using the boundary Yang-Baxter equations. We find a new one-parameter family of the reflection matrices for the RSOS model in addition to the previous result obtained in Ahn C and Koo W M 1996 Nucl. Phys. B 468 [FS] 461. We also find three classes of the reflection matrices for the SOS model, which has one or two free parameters. For the hard-hexagon model which can be mapped to the RSOS(5) model by folding four RSOS heights into two, the solutions can be obtained similarly with a main difference in the boundary unitarity conditions. Due to this, the reflection matrices can have two free parameters. We show that these extra terms can be identified with the `decorated' solutions. We also generalize the hard hexagon model by `folding' the RSOS heights of the general RSOS( p ) model and show that they satisfy the integrability conditions such as the Yang-Baxter and boundary Yang-Baxter equations. These models can be solved using the results for the RSOS models.