Abstract
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 (ABF) models, for which we obtain diagonal, elliptic solutions to the reflection equations, and find that the double-row transfer matrices satisfy functional equations with the same form as in the case of periodic boundary conditions.
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Behrend, R.E., Pearce, P.A. & O'Brien, D.L. Interaction-round-a-face models with fixed boundary conditions: The ABF fusion hierarchy. J Stat Phys 84, 1–48 (1996). https://doi.org/10.1007/BF02179576
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DOI: https://doi.org/10.1007/BF02179576