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 alpha(s) = 2 - pi/2 mu and alpha(1) = 1 - 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.