Capillary waves on anε-dimensional interface

Calculations on the field-theoretic model of an interface, recently proposed by Wallace and Zia, are extended to three-loop order, in an expansion in $\epsilon =d-1\mathrm{}$, where $d$ is the bulk dimension. Extended to $d=2\mathrm{}$, we find a correlation-length exponent $\nu =1\mathrm{}$ near the critical point, in satisfying agreement with the two-dimensional Ising model. We also prove a Ward identity for the Gibbs free energy of the interface which allows a dramatic reduction of the calculational labor involved.