Crossover scale of the fixed point with replica symmetry breaking in the random Potts model

Abstract

We study the scaling properties of the renormalization group (RG) flows in the two-dimensional random Potts model, assuming a general type of replica symmetry breaking (RSB) in the renormalized coupling matrix. It is shown that in the asymptotic regime the RG flows approach the non-trivial RSB fixed point algebraically slowly, which reflects the fact that this type of the fixed point is marginally stable. As a consequence, the crossover spatial scale corresponding to the critical regime described by this fixed point turns out to be exponentially large.