Exact solution of cyclic solid-on-solid lattice models

Paul A. Pearce, Murray T. Batchelor

Franz G. Mertens

Yu‐Kui Zhou, Murray T. Batchelor

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 eigenspectra of the unfused transfer matrix is obtained from the functional relations using the analytic Bethe ansatz. For a special case of crossing parameter , the finite-size corrections to the eigenspectra 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, and , where coprime to L. These results are in agreement with the scaling relations and .

Hector J. de Vega, Esther Lopes

Таичиро Такаги

An exact solution of the local state probability (spontaneous magnetization) of a fusion cyclic solid-on-solid (CSOS) model is obtained for a special (2-fusion) case. It is composed of ratios of theta functions and branching coefficients. Using the modular property its critical behaviour is analysed. In addition, a conjecture for the local state probability of the N-fusion CSOS model is proposed.

Lei Gong-Yan