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 $α_s = 2 - \fracπ{2μ}$ and $α_1 = 1 - \fracπμ$, where $μ$ controls the strength of the four-spin interaction. These values reduce to the known Ising exponents at the decoupling point $μ=π/2$ and confirm the scaling relations $α_s = α_b + ν$ and $α_1 = α_b -1$.