We study homogeneous nucleation in the two-dimensional $q$-state Potts model for $q=3,5,10,20$ and ferromagnetic couplings $J_{ij}\propto \mathrm{\Theta }(R-|i-j\left|\right)$ by means of Monte Carlo simulations employing heat bath dynamics. Metastability is induced in the low-temperature phase through an instantaneous quench of the magnetic field coupled to one of the $q$ spin states. The quench depth is adjusted, depending on the value of temperature $T$, interaction range $R$, and number of states $q$, in such a way that a constant nucleation time is always obtained. In this setup, we analyze the crossover between the classical compact droplet regime occurring in the presence of short-range interactions $R\sim 1$ and the long-range regime $R\gg 1$ where the properties of nucleation are influenced by the presence of a mean-field spinodal singularity. We evaluate the metastable susceptibility of the order parameter as well as various critical droplet properties, which along with the evolution of the quench depth as a function of $q,T$ and $R$ are then compared with the field theoretical predictions valid in the large $R$ limit to find the onset of spinodal-assisted nucleation. We find that, with a mild dependence of the values of $q$ and $T$ considered, spinodal scaling holds for interaction ranges $R\gtrsim 8-10$ and that signatures of the presence of a pseudospinodal are already visible for remarkably small interaction ranges $R\sim 4-5$. The influence of spinodal singularities on the occurrence of multistep nucleation is also discussed.

• Received 5 April 2021
• Accepted 7 June 2021

DOI:https://doi.org/10.1103/PhysRevE.104.014115