Interface fluctuations in disordered systems: 5-epsilon expansion and failure of dimensional reduction.

A functional renormalization group 5-epsilon expansion is used to calculate the exponent, zeta, which measures the roughness of an interface in a disordered Ising system as a function of length scale. Formal dimensional reduction is explicitly shown to breakdown at leading order in epsilon. For random field disorder we obtain zeta = epsilon/3 resolving the discrepancy between various previous calculations, and for random bond disorder, we find zeta = 0.2083 epsilon.