We study the low temperature quench dynamics of the two-dimensional Potts model in the limit of a large number of states, q ≫ 1. We identify a q-independent crossover temperature (the pseudo spinodal) below which no high-temperature metastability stops the curvature driven coarsening process. At short length scales, the latter is decorated by freezing for some lattice geometries, notably the square one. With simple analytic arguments, we evaluate the relevant time-scale in the coarsening regime, which turns out to be of Arrhenius form and independent of q for large q. Once taken into account, dynamic scaling is universal.

We study the bidimensional q-Potts model with long-range bond correlated disorder. Similarly to Chatelain (2014 Phys. Rev. E 89 032105), we implement a disorder bimodal distribution by coupling the Potts model to auxiliary spin-variables, which are correlated with a power-law decaying function. The universal behaviour of different observables, especially the thermal and the order-parameter critical exponents, are computed by Monte-Carlo techniques for q = 1 , 2 , 3 -Potts models for different values of the power-law decaying exponent a. On the basis of our conclusions, which are in agreement with previous theoretical and numerical results for q = 1 and q = 2, we can conjecture the phase diagram for q ∈ [ 1 , 4 ] . In particular, we establish that the system is driven to a fixed point at finite or infinite long-range disorder depending on the values of q and a. Finally, we discuss the role of the higher cumulants of the disorder distribution. This is done by drawing the auxiliary spin-variables from different statistical models. While the main features of the phase diagram depend only on the first and second cumulant, we argue, for the infinite disorder fixed point, that certain universal effects are affected by the higher cumulants of the disorder distribution.

We study the bi-dimensional q-Potts model with long-range bond correlated disorder. Similarly to [1], we implement a disorder bimodal distribution by coupling the Potts model to auxiliary spin-variables, which are correlated with a power-law decaying function. The universal behaviour of different observables, especially the thermal and the order-parameter critical exponents, are computed by Monte-Carlo techniques for q = 1, 2, 3-Potts models for different values of the power-law decaying exponent a. On the basis of our conclusions, which are in agreement with previous theoretical and numerical results for q = 1 and q = 2, we can conjecture the phase diagram for q ∈ [1, 4]. In particular, we establish that the system is driven to a fixed point at finite or infinite long-range disorder depending on the values of q and a. Finally, we discuss the role of the higher cumulants of the disorder distribution. This is done by drawning the auxiliary spin-variables from different statistical models. While the main features of the phase diagram depend only on the first and second cumulant, we argue, for the infinite disorder fixed point, that certain universal effects are affected by the higher cumulants of the disorder distribution.

We study the quench dynamics of the q Potts model on different bi/tri-dimensional lattice topologies. In particular, we are interested in instantaneous quench from T i → ∞ to T ⩽ T s , where T s is the (pseudo)-spinodal temperature. The goal is to explain why, in the large-q limit, the low-temperature dynamics freezes on some lattices while on others the equilibrium configuration is easily reached. The cubic (3d) and the triangular (2d) lattices are analysed in detail. We show that the dynamics blocks when lattices have acyclic unitary structures while the system goes to the equilibrium when these are cyclic, no matter the coordination number (z) of the particularly considered lattice.