2009/05/01 by Takashi Mori, Seiji Miyashita, Per Arne Rikvold · 3 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Bistability #Critical point (mathematics) #Differential equation #Fokker–Planck equation #Kinetic Monte Carlo #Master equation #Mathematical analysis #Mathematics #Monte Carlo method #Phase (matter) #Physics #Quantum #Quantum mechanics #Relaxation (psychology) #Scaling #Spinodal #Spinodal decomposition #Statistical physics #Theoretical and Computational Physics #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physreve.81.011135
published as Phys. Rev. E 81, 011135 (2010) · 11 pages, 4 figures, title is changed
openalex publication_date 2010/01/27 · arxiv created 2013/06/20 · arxiv updated 2015/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study critical properties of the relaxation time at a threshold point in switching processes between bistable states under change in 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 re-examine 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 photoexcitation processes in spin-crossover materials. In the ongoing development of nanosize 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.