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 α_s = 2 − π/2μ and α₁ = 1 − π/2μ, 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 + v and α₁ = α_b − 1.