On superuniversality in the q-state Potts model with quenched disorder

We obtain the exact scale invariant scattering solutions for two-dimensional field theories with replicated permutational symmetry Sq. After sending to zero the number of replicas they correspond to the renormalization group fixed points of the q-state Potts model with quenched disorder. We find that all solutions with non-zero disorder possess q-independent sectors, pointing to superuniversality (i.e. symmetry independence) of some critical exponents. The solution corresponding to the random bond ferromagnet, for which disorder vanishes as q→2, allows for superuniversality of the correlation length exponent ν [PRL 118 (2017) 250601]. Of the two solutions which are strongly disordered for all values of q, one is completely q-independent and accounts for the zero-temperature percolation fixed point of the randomly bond diluted ferromagnet. The other is the main candidate to describe the Nishimori-like fixed point of the Potts model with ±J disorder, and leaves room for superuniversality of the magnetic exponent η, a possibility not yet excluded by available numerical data.