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

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 $δ>δ_t$ 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 $δ_t$ is the tricritical disorder, which separates the first- and second-order transition regimes. The tricritical exponents are estimated as $β_t/ν_t=0.10(2)$ and $ν_t=0.67(4)$. We claim these exponents are $q$ independent, for sufficiently large $q$. In the second-order transition regime the critical exponents $β_t/ν_t=0.60(2)$ and $ν_t=0.73(1)$ are independent of the strength of disorder.