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

Bravyi S.B., Dotsenko V.S.

**We study the scaling properties of the renormalization group (RG) flows in the two-dimensional random Potts model assuming general type of the 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 such type of t ie 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.** **PACS: 05.50.+q, ****05.70.Fh****, 75.10.Hk**