Spinodal-like scaling behavior after a temperature quench across the first-order phase transition in three-dimensional $q$-state Potts models

TL;DR

This study investigates the out-of-equilibrium spinodal-like behavior in 3D q-state Potts models after a temperature quench across the first-order transition, revealing a specific scaling law and supporting numerical evidence.

Contribution

It introduces a novel scaling law for energy density evolution post-quench and provides numerical validation for spinodal-like behavior in 3D Potts models.

Findings

Energy density scales with (\ln t)^{3/2} \, \\delta

Discontinuity at a specific \\rho_s>0 indicates spinodal-like behavior

Time scale \\tau increases exponentially as \\ln \\tau \\approx (\\ ho_s/\\delta)^{2/3}

Abstract

We study the out-of-equilibrium spinodal-like behavior of three-dimensional (3D) $q$-state Potts models (for $q\ge 3$), observed when the temperature is quenched across the first-order transition (FOT) point $\beta_{\rm fo}=T_{\rm fo}^{-1}$. We consider a standard quench protocol, in which high-temperature configurations, thermalized at $\beta_i<\beta_{\rm fo}$, are driven across the FOT by a purely relaxational dynamics at $\beta>\beta_{\rm fo}$. We focus on the emergence of spinodal-like behaviors in the thermodynamic limit, associated with the dynamic phase change. We argue that, if the nucleation of smooth droplets is the relevant mechanism of the post-quench phase change, for sufficiently small $\beta_{\rm fo}-\beta_i>0$, the time-dependent energy density should scale in terms of $\rho = (\ln t)^{3/2} \delta$, where $\delta = \beta/\beta_{\rm fo}-1$, with a discontinuity at a particular value $\rho=\rho_s>0$. This implies the emergence of a spinodal-like behavior, whose time scale $\tau$ increases exponentially as $\ln \tau \approx (\rho_s/\delta)^{2/3}$ in the limit $\delta\to 0^+$. We present a numerical analysis of the quench protocol in the 3D $q=6$ Potts model, which supports the above spinodal-like scenario.