Euclidean Group as a Dynamical Symmetry of Surface Fluctuations: The Planar Interface and Critical Behavior

The statistical mechanics of the interface between two discrete thermodynamic phases is studied in terms of a field f which describes the deviation of the interface from planar. Exploiting the dynamical Euclidean invariance of the Hamiltonian of the field f, we construct ε expansions for Ising-like critical behavior in 1+ε dimensions, with a critical temperature of order ε, Scaling functions for the interface profile and width in a pinning potential are obtained.