Analytic structures of unitary RSOS models with integrable boundary conditions

TL;DR

This paper analyzes the analytic structure of eigenvalues in the unitary RSOS lattice model with integrable boundaries, using transfer matrices and comparing with Ising models.

Contribution

It introduces a commuting transfer matrix for the RSOS model and studies its eigenvalue structure, providing new insights into boundary integrable models.

Findings

Eigenvalue zero configurations are characterized and visualized.

The transfer matrix satisfies universal functional relations.

Comparative analysis with Ising models highlights similarities and differences.

Abstract

In this paper, we consider the unitary critical restricted-solid-on-solid (RSOS) lattice $\mathcal{M}(5,6)$ model with integrable boundary conditions. We introduce its commuting double row transfer matrix satisfying the universal functional relations, and we use it in order to study the analytic structure of the transfer matrix eigenvalues and plot representative zero configurations of sample eigenvalues of the transfer matrix. We finally conclude with a comparative analysis with the critical and tricritical Ising models with integrable boundary conditions.