spin update trials, according to the Metropolis algorithm). Within his analysis he was unable to distinguish between two different scenarios for the transition at $q \geq 5$ due to finite size effects taking place at the simulations. He proposed two self-avoiding possible scenarios for the transition. In the first one the energy per spin reaches the transition temperature with a finite slope both coming from higher and lower temperatures, thus projecting metastable branches at both sides of the transition that end at temperatures $T_{sp}^+$ and $T_{sp}^-$ both different from $T_c$. In the second scenario, the energy reaches $T_c$ with an infinite slope which would imply a first order phase transition with a true divergence of the specific heat at $T_c$.

On the other hand, other approaches based on different definitions of the spinodal temperatures predict, either the convergence of the finite size spinodal temperatures to $T_c$ [@MeMo2000; @BaBeDu2008] or a convergence to limit values different from but closely located to $T_c$ [@LoFeGrCa2009].

Optimized GPU-based Monte Carlo algorithm for the q-state Potts model {#algorithm}
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We developed a GPU based code to simulate the two dimensional Potts model, using classical Metropolis dynamics on square lattices of size $N= L \times L$ 