Asymptotic forms and scaling properties of the relaxation time near threshold points in spinodal-type dynamical phase transitions

TL;DR

This paper investigates the divergence and scaling of relaxation times near spinodal points in bistable systems, using analytical, numerical, and simulation methods, with applications to photo-excitation in spin-crossover materials.

Contribution

It provides a detailed analysis of the asymptotic forms and scaling properties of relaxation times near critical points in spinodal-type transitions, extending to transient phenomena under external perturbations.

Findings

Relaxation time diverges near the spinodal point following specific asymptotic forms.

Scaling relations are confirmed through numerical solutions and simulations.

The results are applicable to photo-excitation processes in spin-crossover materials.

Abstract

We study critical properties of the relaxation time at a threshold point in switching processes between bistable states under change of external fields. In particular, we investigate the relaxation processes near the spinodal point of the infinitely long-range interaction model (the Husimi-Temperley model) by analyzing the scaling properties of the corresponding Fokker-Planck equation. We also confirm the obtained scaling relations by direct numerical solution of the original master equation, and by kinetic Monte Carlo simulation of the stochastic decay process. In particular, we study the asymptotic forms of the divergence of the relaxation time near the spinodal point, and reexamine its scaling properties. We further extend the analysis to transient critical phenomena such as a threshold behavior with diverging switching time under a general external driving perturbation. This models photo-excitation processes in spin-crossover materials. In the ongoing development of nano-size fabrication, such size-dependence of switching processes should be an important issue, and the properties obtained here will be applicable to a wide range of physical processes.