Surface Critical Phenomena and Scaling in the Eight-Vertex Model

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 αₛ0ex0ex=0ex0ex2-π/2μ and α₁0ex0ex=0ex0ex1-π/μ, where {μ} controls the strength of the four-spin interaction. These values reduce to the known Ising exponents at the decoupling point μ0ex0ex=0ex0exπ/2 and confirm the scaling relations αₛ0ex0ex=0ex0exαb+ν and α₁0ex0ex=0ex0exαb-1.