Spinodal-assisted nucleation in the two-dimensional q-state Potts model with short-to-long-range interactions

We study homogeneous nucleation in the two-dimensional q-state Potts model for q=3,5,10,20 and ferromagnetic couplings J_{ij}∝Θ(R-|i-j|) 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∼1 and the long-range regime R≫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≳8-10 and that signatures of the presence of a pseudospinodal are already visible for remarkably small interaction ranges R∼4-5. The influence of spinodal singularities on the occurrence of multistep nucleation is also discussed.