Freezing vs. equilibration dynamics in the Potts model

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