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Dynamical heterogeneities as fingerprints of a backbone structure in Potts models

We investigate slow non-equilibrium dynamical processes in two-dimensional $q$--state Potts model with both ferromagnetic and $\pm J$ couplings. Dynamical properties are characterized by means of the mean-flipping time distribution. This quantity is known for clearly unveiling dynamical heterogeneities. Using a two-times protocol we characterize the different time scales observed and relate them to growth processes occurring in the system. In particular we target the possible relation between the different time scales and the spatial heterogeneities originated in the ground state topology, which are associated to the presence of a backbone structure. We perform numerical simulations using an approach based on graphics processing units (GPUs) which permits to reach large system sizes. We present evidence supporting both the idea of a growing process in the preasymptotic regime of the glassy phases and the existence of a backbone structure behind this processes.