Renormalization group and variational treatments for a d-dimensional sine-Gordon model with correlated random fields

We study the effects of correlated symmetry-breaking-like random fields on critical properties of a d-dimensional sine-Gordon model. A Wilsonian renormalization group analysis shows an unusual scenario in the absence of stable fixed points. The physical nature of the related runaway in the parameter space is investigated by means of a complementary variational treatment. Self-consistent predictions for d>1 suggest that the disorder of the type considered here inhibits any phase transition with diverging correlation length and that the system lives in a “glassy-phase” at all temperatures.