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Journal of Statistical Physics

, Volume 84, Issue 1–2, pp 1–48 | Cite as

Interaction-round-a-face models with fixed boundary conditions: The ABF fusion hierarchy

  • Roger E. Behrend
  • Paul A. Pearce
  • David L. O'Brien
Articles

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.

Key Words

Andrews-Baxter-Forrester models exactly solvable lattice models fixed boundary conditions reflection equations Yang-Baxter equation 

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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • Roger E. Behrend
    • 1
  • Paul A. Pearce
    • 1
  • David L. O'Brien
    • 1
  1. 1.Department of MathematicsUniversity of MelbourneParkvilleAustralia

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