The large-N random phase sine-Gordon model

At large distances and in the low-temperature phase, the quenched correlation functions in the 2d random phase sine-Gordon model have been argued to be of the form: [[phi(x) - phi(0)](2)]* = A(log \x\)+B epsilon(2)(log \x\)(2), with epsilon = (T-T-c). However, renormalization group computations predict B not equal 0, while variational approaches (which are supposed to be exact for models with a large number of components) give B = 0. We introduce a large-N version of the random phase sine-Gordon model. Using non-Abelian bosonization and renormalization group techniques, we show that the correlation functions of our models have the above form but with a coefficient B suppressed by a factor 1/N-3 compared to A.