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In this paper we provide new analytic results on two-dimensional $q$-Pottsmodels ($q \geq 2$) in the presence of bond disorder correlations which decayalgebraically with distance with exponent $a$. In particular, our results arevalid for the long-range bond disordered Ising model ($q=2$). We implement arenormalization group perturbative approach based on conformal perturbationtheory. We extend to the long-range case the RG scheme used in [V. Dotsenko,Nucl. Phys. B 455 701 23] for the short-range disorder. Our approach is basedon a $2$-loop order double expansion in the positive parameters $(2-a)$ and$(q-2)$. We will show that the Weinrib-Halperin conjecture for the long-rangethermal exponent can be violated for a non-Gaussian disorder. We compute thecentral charges of the long-range fixed points finding a very good agreementwith numerical measurements.

Two-dimensional Ising and Potts model with long-range bond disorder: a renormalization group approach