Unusual Bifurcation of Renormalization-Group Fixed Points for Interfacial Transitions

Effective Hamiltonians for interfaces which arise, e.g., in the theory of wetting are studied by a nonlinear functional renormalization group exact in linear order and apparantly accurate for all spatial dimensionalities, $d$. Two nontrivial fixed points are found for $d<\mathrm{}3\mathrm{}$ which describe the critical manifold and the completely delocalized phase, respectively. As $d$ varies, these do not bifurcate from the Gaussian fixed point at $d_u=3\mathrm{}$ but rather mutually annihilate leaving behind a line of unusual "drifting" fixed points. Correspondingly the critical exponents exhibit singular behavior as $d\to 3-$.