arXiv subjects

David L. O'Brien

Publications and source records attributed to David L. O'Brien.

3 recordsLinked to original sources

arXiv1996

Surface Free Energies, Interfacial Tensions and Correlation Lengths of the ABF Models

The surface free energies, interfacial tensions and correlation lengths of the Andrews-Baxter-Forrester models in regimes III and IV are calculated with fixed boundary conditions. The interfacial tensions are calculated between arbitrary phases and are shown to be additive. The associated critical exponents are given by $2-α_s=μ=ν$ with $ν=(L+1)/4$ in regime III and $4-2α_s=μ=ν$ with $ν=(L+1)/2$ in regime IV. Our results are obtained using general commuting transfer matrix and inversion relation methods that may be applied to other solvable lattice models.

cond-mat↗

arXiv1995

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

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 $α_s=(7-L)/4$ is independent of the choice of boundary.

cond-mat↗

arXiv1995

Interaction-Round-a-Face Models with Fixed Boundary Conditions: The ABF Fusion Hierarchy

We use boundary weights and reflection equations to obtain families of commuting double-row transfer matrices for interaction-round-a-face models with fixed boundary conditions. In particular, we consider the fusion hierarchy of the Andrews-Baxter-Forrester models, for which we find that the double-row transfer matrices satisfy functional equations with an su(2) structure.

hep-th↗