Disordered O(n)O(n) loop model and coupled conformal field theories

A family of models for fluctuating loops in a two-dimensional random background is analyzed. The models are formulated as O(n)O(n) spin models with quenched inhomogeneous interactions. Using the replica method, the models are mapped to the M→0M→0 limits of M  -layered O(n)O(n) models coupled each other via ϕ1,3ϕ1,3 primary fields. The renormalization group flow is calculated in the vicinity of the decoupled critical point, by an epsilon expansion around the Ising point (n=1n=1), varying n   as a continuous parameter. The one-loop beta function suggests the existence of a strongly coupled phase (0