Surface Free Energies and Surface Critical Behaviour of the ABF Models with Fixed Boundaries

Abstract

In a previous paper, we introduced reflection equations for interaction-round-a-face (IRF) models and used these to construct commuting double-row transfer matrices for solvable lattice spin models with fixed boundary conditions. In particular, for the Andrews-Baxter-Forrester (ABF) models, we derived special functional equations satisfied by the eigenvalues of the commuting double-row transfer matrices. Here we introduce a generalized inversion relation method to solve these functional equations for the surface free energies. Although the surface free energies depend on the boundary spins we find that the associated surface critical exponent ${\alpha }_s=(7-L)/4$ is independent of the choice of boundary.

10 pages, latex2e with the amsmath and amsfonts packages

References in corpus (6)

• Interaction-Round-a-Face Models with Fixed Boundary Conditions: The ABF Fusion Hierarchy
• Boundary Yang-Baxter equation in the RSOS/SOS representation
• Surface Critical Phenomena and Scaling in the Eight-Vertex Model
• An Ising model in a magnetic field with a boundary
• Exact solution and surface critical behaviour of open cyclic SOS lattice models
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• Excited TBA Equations I: Massive Tricritical Ising Model
• The bulk, surface and corner free energies of the square lattice Ising model
• Entanglement Entropy from Corner Transfer Matrix in Forrester Baxter non-unitary RSOS models
• Finite-Volume Spectra of the Lee-Yang Model
• Correlation lengths and E_8 mass spectrum of the dilute A_3 lattice model
• Integrable and Conformal Boundary Conditions for Z_k Parafermions on a Cylinder
• Kac boundary conditions of the logarithmic minimal models
• Critical site percolation on the triangular lattice: From integrability to conformal partition functions
• Approaching the RSOS critical points through entanglement: one model for many universalities
• Logarithmic Minimal Models with Robin Boundary Conditions
• Integrable Boundaries and Universal TBA Functional Equations
• On the critical boundary RSOS \mathcal{M}(3,5) model
• Boundary reflection matrices of massive ${\varphi }_{1,3}$-perturbed unitary minimal models