We study the critical behavior of the q-state Potts model in the presence of quenched random fields, which locally prefer ordering of any one of the q states, and are long-range correlated such that [H(0)H(R${\left)\right]}_{\mathrm{av}\mathrm{\sim }{R}^{\mathrm{-}\left(d\mathrm{-}\theta \right)}}$. We find a stable critical behavior controlled by a new random fixed point, and obtain a set of critical exponents within the ε̃ expansion (ε̃=8+θ-d), which cannot be related to those of a pure Potts model of lower dimensionality.

• Received 5 March 1985

DOI:https://doi.org/10.1103/PhysRevB.32.350