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 Ji j oc O(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 ti 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 ti 4 - 5. The influence of spinodal singularities on the occurrence of multistep nucleation is also discussed.

Automated summary

In this study, homogeneous nucleation in the two-dimensional q-state Potts model was investigated through Monte Carlo simulations. By adjusting the quench depth, temperature, and number of states, the crossover between short-range and long-range interactions in nucleation properties was analyzed. Spinodal scaling was found to hold for interaction ranges above 8-10, with signs of pseudospinodal visible for interaction ranges as small as 4-5.