On different approaches to integrable lattice models

Vladimir Belavin, Doron Gepner, J. Ramos Cabezas, Boris Runov

Research output: Contribution to journalArticlepeer-review


Interaction-round the face (IRF) models are two-dimensional lattice models of statistical mechanics defined by an affine Lie algebra and admissibility conditions depending on a choice of representation of that affine Lie algebra. Integrable IRF models, i.e. the models the Boltzmann weights of which satisfy the quantum Yang-Baxter equation, are of particular interest. In this paper, we investigate trigonometric Boltzmann weights of integrable IRF models. By using an ansatz proposed by one of the authors in some previous works, the Boltzmann weights of the restricted IRF models based on the affine Lie algebras su ( 2 ) k and su ( 3 ) k are computed for fundamental and adjoint representations for some fixed levels k. New solutions for the Boltzmann weights are obtained. We also study the vertex-IRF correspondence in the context of an unrestricted IRF model based on su ( 3 ) k (for general k) and discuss how it can be used to find Boltzmann weights in terms of the quantum R ^ matrix when the adjoint representation defines the admissibility conditions.

Original languageEnglish
Article number155201
JournalJournal of Physics A: Mathematical and Theoretical
Issue number15
StatePublished - 12 Apr 2024


  • CFT
  • approaches
  • integrable lattice models
  • interaction-round the face models
  • lattice
  • models


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