A Method to Study Relaxation of Metastable Phases: Macroscopic Mean-Field Dynamics

Abstract

We propose two different macroscopic dynamics to describe the decay of metastable phases in many-particle systems with local interactions. These dynamics depend on the macroscopic order parameter $m$ through the restricted free energy $F(m)$ and are designed to give the correct equilibrium distribution for $m$. The connection between macroscopic dynamics and the underlying microscopic dynamic are considered in the context of a projection- operator formalism. Application to the square-lattice nearest-neighbor Ising ferromagnet gives good agreement with droplet theory and Monte Carlo simulations of the underlying microscopic dynamic. This includes quantitative agreement for the exponential dependence of the lifetime on the inverse of the applied field $H$, and the observation of distinct field regions in which the derivative of the lifetime with respect to $1/H$ depends differently on $H$. In addition, at very low temperatures we observe oscillatory behavior of this derivative with respect to $H$, due to the discreteness of the lattice and in agreement with rigorous results. Similarities and differences between this work and earlier works on finite Ising models in the fixed-magnetization ensemble are discussed.

44 pages RevTeX3, 11 uuencoded Postscript figs. in separate file.

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• Metastability in the two-dimensional Ising model with free boundary conditions
• A projection method for statics and dynamics of lattice spin systems
• Monte Carlo study of the evaporation/condensation transition on different Ising lattices
• Simulations of metastable decay in two- and three-dimensional models with microscopic dynamics
• A new time quantifiable Monte Carlo method in simulating magnetization reversal process
• Extreme Long-time Dynamic Monte Carlo Simulations
• Advanced Dynamic Algorithms for the Decay of Metastable Phases in Discrete Spin Models: Bridging Disparate Time Scales
• Application of the Projected Dynamics Method to an Anisotropic Heisenberg Model
• Solving the Master Equation for Extremely Long Time Scale Calculations
• Free energy and metastable states in the square-lattice $J_1$-$J_2$ Ising model
• Usefulness of an equal-probability assumption for out-of-equilibrium states: a master equation approach
• Dynamics of Desorption with Lateral Diffusion
• Projected single-spin flip dynamics in the Ising Model