Square-lattice random potts model: Criticality and pitchfork bifurcation

Within a real space renormalization group framework based on self-dual clusters, we discuss the criticality of the quenched bond-mixed q-state Potts ferromagnet on a square lattice. On qualitative grounds we exhibit that crossover from the pure fixed point to the random one occurs, while q increases, through a pitchfork bifurcation; the relationship with the Harris criterion is analyzed. On quantitative grounds we present high precision numerical values for the critical temperatures corresponding to various concentrations of the coupling constants J1 and J2, and various ratios J1/J2. The pure, random and crossover critical exponents are discussed as well.