Row transfer matrix spectra of cyclic solid-on-solid lattice models

D Kim, Paul A. Pearce

The operator content of the cyclic solid-on-solid models is derived under general boundary conditions by mapping the row-to-row transfer matrix onto the six-vertex model and XXZ Heisenberg chain. For the shift boundary conditions, the dimensions and spins of the primary operators are derived analytically from finite-size corrections to the scaling spectra. The full operator content agrees with results for a quantum chain model having the same local symmetry.

Tetsuji Miwa

Omar El Deeb

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.

Kush Saha

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 .