$q$-state Potts model [@Wu1982] without external fields is defined by the Hamiltonian

$$H = - J \sum_{<i,j>} \delta (s_i,s_j) \label{Hamiltonian}$$

where $s_i=1,2,\ldots,q$, $\delta (s_i,s_j)$ is the Kronecker delta and the sum runs over all nearest neighbors pairs of spins in a Bravais lattice with $N$ sites. Being a generalization of the Ising model ($q=2$), this model displays a richer behavior than the former. One of the main interests is that the two-dimensional ferromagnetic version ($J>0$) exhibit a first order phase transition at some finite temperature when $q>4$, while for $q\leq 4$ the transition is continuous [@Wu1982]. Hence, it has become a paradigmatic model in the study of phase transitions and their associated dynamics, like for instance, domain growth kinetics [@ViGr1987; @GrAnSr1988; @SiMa1995b; @FeCa2007; @LoArCuSi2010] and nucleation as an equilibration mechanism [@MeMo2000; @Ru2002; @BaGuTrTrHu2010].

Some equilibrium properties of the two-dimensional model are known exactly, which allows numerical algorithms testing. We list here some of them that are used for comparison with the numerical results in the present work. For instance, the transition temperature for the square lattice in the thermodynamic limit is given by [@Ba1973]

$$\label{Tc}
    \frac{k_B T_c}{J} = \frac{1}{\ln (1+\sqrt{q})}$$

where $k_B$ is the Boltzmann constant. Hereafter we will choose 