Universality class of replica synchronization transition of smooth coupled map lattices in the presence of quenched disorder

Synchronization of two replicas of coupled map lattices for continuous maps is known to be in the multiplicative noise universality class. We study this transition in presence of identical quenched disorder in coupling in both replicas for coupled logistic and tent maps. We study one-dimensional, two-dimensional, and globally coupled cases. We observe a clear second-order transition with new exponents. The order parameter decays as $t^{-\delta}$ with $\delta=2$ for tent map and $\delta=3$ for logistic map in any dimension. The asymptotic order parameter grows as $\Delta^{\beta}$ with $\beta=2$ for the tent map and $\beta=3$ for the logistic map. The quenched disorder in coupling is a relevant perturbation for the replica synchronization of coupled map lattices. The critical exponents are different from that of the multiplicative noise universality class. We observe that the critical exponents are independent of dimensions and super-universal in nature