Surface Critical Phenomena and Scaling in the Eight-Vertex Model

Abstract

We give a physical interpretation of the entries of the reflection $K$-matrices of Baxter's eight-vertex model in terms of an Ising interaction at an open boundary. Although the model still defies an exact solution we nevertheless obtain the exact surface free energy from a crossing-unitarity relation. The singular part of the surface energy is described by the critical exponents ${\alpha }_s=2-\frac{\pi }{2\mu }$ and ${\alpha }_1=1-\frac{\pi }{\mu }$, where $\mu$ controls the strength of the four-spin interaction. These values reduce to the known Ising exponents at the decoupling point $\mu =\pi /2$ and confirm the scaling relations ${\alpha }_s={\alpha }_b+\nu$ and ${\alpha }_1={\alpha }_b-1$.

12 pages, LaTeX with REVTEX macros needed. To appear in Physical Review Letters

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• Exact solution and surface critical behaviour of open cyclic SOS lattice models
• Fateev-Zamolodchikov and Kashiwara-Miwa models: boundary star-triangle relations and surface critical properties
• Surface Critical Phenomena in Interaction-Round-a-Face Models