Scaling properties of the relaxation time near the mean-field spinodal

Abstract

We study the relaxation processes of the infinitely long-range interaction model (the Husimi-Temperley model) near the spinodal point. We propose a unified finite-size scaling function near the spinodal point, including the metastable region, the spinodal point, and the unstable region. We explicitly adopt the Glauber dynamics, derive a master equation for the probability distribution of the total magnetization, and perform the so-called van Kampen Omega expansion (an expansion in terms of the inverse of the systems size), which leads to a Fokker-Planck equation. We analyze the scaling properties of the Fokker-Planck equation and confirm the obtained scaling plot by direct numerical solution of the original master equation, and by kinetic Monte Carlo simulation of the stochastic decay process.

9 pages, 3 figures

References in corpus (4)

• Realization of the mean-field universality class in spin-crossover materials
• Structure of Metastable States in Phase Transitions with High-Spin Low-Spin Degree of Freedom
• Non-equilibrium Characterization of Spinodal Points using Short Time Dynamics
• Threshold Phenomena under Photo Excitation of Spin-crossover Materials with Cooperativity due to Elastic Interactions

Cited by in corpus (22)

• Evolution of opinions on social networks in the presence of competing committed groups
• Analysis of the exactness of mean-field theory in long-range interacting systems
• Crossover between a Short-range and a Long-range Ising model
• Critical Slowing Down at the Abrupt Mott Transition: When the First-Order Phase Transition Becomes Zeroth-Order and Looks Like Second-Order
• Non-contact Friction and Relaxational Dynamics of Surface Defects
• Equilibrium, Metastability, and Hysteresis in a Model Spin-crossover Material with Nearest-neighbor Antiferromagnetic-like and Long-range Ferromagnetic-like Interactions
• Monte Carlo Simulations of the Critical Properties of a Ziff-Gulari-Barshad model of Catalytic CO Oxidation with Long-range Reactivity
• Nontrivial phase diagram for an elastic interaction model of spin crossover materials with antiferromagnetic-like short-range interactions
• Dynamic hysteresis at a noisy saddle-node shows power-law scaling but nonuniversal exponent
• Short-time dynamics of finite-size mean-field systems
• Phase diagrams and free-energy landscapes for model spin-crossover materials with antiferromagnetic-like nearest-neighbor and ferromagnetic-like long-range interactions
• Quantum Stoner-Wohlfarth model
• Nonequilibrium thermodynamic process with hysteresis and metastable states -- A contact Hamiltonian with unstable and stable segments of a Legendre submanifold
• Dynamical phase transition in Floquet optical bistable systems: An approach from finite-size quantum systems
• Coercivity Landscape Characterizes Dynamic Hysteresis
• Finite-time and Finite-size scalings of coercivity in dynamic hysteresis
• Effective Hamiltonian approach to kinetic Ising models: Application to an infinitely long-range Husimi-Temperley model
• Spinodal-assisted nucleation in the two-dimensional $q-$state Potts model with short-to-long range interactions
• Existence of shape-dependent thermodynamic limit in spin systems with short- and long-range interactions
• Distribution of eigenstate populations and dissipative beating dynamics in uniaxial single-spin magnets
• Analysis of finite-size effect of infinite-range Ising model under Glauber dynamics
• Analysis of the finite-size effect of the long-range Ising model under Glauber dynamics