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

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 ${\beta }_{\mathrm{fo}}=T_{\mathrm{fo}}^{-1}$. We consider a standard quench protocol, in which high-temperature configurations, thermalized at ${\beta }_i<{\beta }_{\mathrm{fo}}$, are driven across the FOT by a purely relaxational dynamics at $\beta >{\beta }_{\mathrm{fo}}$. 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 ${\beta }_{\mathrm{fo}}-{\beta }_i>0$, the time-dependent energy density should scale in terms of $\rho =(\ln t{)}^{3/2}\delta$, where $\delta =\beta /{\beta }_{\mathrm{fo}}-1$, 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.

8 pages, 3 figures. Corrected misprints

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