Critical and tricritical singularities of the three-dimensional random-bond Potts model for large q

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We study the effect of varying strength, δ, of bond randomness on the phase transition of the three-dimensional Potts model for large q. The cooperative behavior of the system is determined by large correlated domains in which the spins points into the same direction. These domains have a finite extent in the disordered phase. In the ordered phase there is a percolating cluster of correlated spins. For a sufficiently large disorder δ>δₜ this percolating cluster coexists with a percolating cluster of non-correlated spins. Such a co-existence is only possible in more than two dimensions. We argue and check numerically that δₜ is the tricritical disorder, which separates the first- and second-order transition regimes. The tricritical exponents are estimated as βₜ/νₜ=0.10(2) and νₜ=0.67(4). We claim these exponents are q independent, for sufficiently large q. In the second-order transition regime the critical exponents βₜ/νₜ=0.60(2) and νₜ=0.73(1) are independent of the strength of disorder.