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

TL;DR

This study investigates how the range of interactions affects nucleation in the 2D q-state Potts model, revealing the onset of spinodal-assisted nucleation at moderate interaction ranges through Monte Carlo simulations.

Contribution

It provides the first detailed numerical analysis of the crossover from classical to spinodal-assisted nucleation in the Potts model with variable interaction range.

Findings

Spinodal scaling observed for R ≥ 8-10.

Signatures of pseudo-spinodal appear at R ≈ 4-5.

Interaction range influences nucleation pathways.

Abstract

We study homogeneous nucleation in the two-dimensional $q-$state Potts model for $q=3,5,10,20$ and ferromagnetic couplings $J_{ij} \propto \Theta (R - |i-j|)$, 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 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 in order to find the onset of spinodal-assisted nucleation. We find that, with a mild dependence on 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 pseudo-spinodal are already visible for remarkably small interaction ranges $R\sim 4-5$. The influence of spinodal singularities on the occurrence of multi-step nucleation is also discussed.