Exact solution and surface critical behaviour of open cyclic SOS lattice models

TL;DR

This paper provides an exact solution for open cyclic SOS lattice models, analyzing their surface critical behavior and deriving surface free energy exponents using integrable boundary conditions and Bethe ansatz methods.

Contribution

It introduces the integrable boundary face weights for open boundary conditions and computes surface critical exponents for these models.

Findings

Finite-size corrections yield conformal dimensions.

Surface free energy calculations produce specific heat exponents.

Results agree with known scaling relations.

Abstract

We consider the $L$-state cyclic solid-on-solid lattice models under a class of open boundary conditions. The integrable boundary face weights are obtained by solving the reflection equations. Functional relations for the fused transfer matrices are presented for both periodic and open boundary conditions. The eigen-spectra of the unfused transfer matrix is obtained from the functional relations using the analytic Bethe ansatz. For a special case of crossing parameter $\lambda=\pi/L$, the finite-size corrections to the eigen-spectra of the critical models are obtained, from which the corresponding conformal dimensions follow. The calculation of the surface free energy away from criticality yields two surface specific heat exponents, $\alpha_s=2-L/2\ell$ and $\alpha_1=1-L/\ell$, where $\ell=1,2,\cdots,L-1$ coprime to $L$. These results are in agreement with the scaling relations $\alpha_s=\alpha_b+\nu$ and $\alpha_1=\alpha_b-1$.