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

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

1996-02-14

arxiv.org/abs/cond-mat/9602078v1

J. Phys. A 29 (1996) 1987

Physics

Condensed Matter

13 pages, LaTeX, to appear in J. Phys. A

Scientific paper

10.1088/0305-4470/29/9/014

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 $\alpha_1=\alpha_b-1$.

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