Phase prediction method for pattern formation in time-dependent Ginzburg-Landau dynamics for kinetic Ising model without a priori assumptions of domain patterns

摘要

We propose a phase prediction method for pattern formation in a two-dimensional kinetic Ising model with dipole-dipole interactions under the time-dependent Ginzburg-Landau dynamics. Considering the effects of the material thickness by assuming uniformness along the magnetization axis, the model corresponds to thin magnetic materials with long-range repulsive interactions. We formulate a theoretical basis to understand the effects of the material parameters on the formation of the magnetic domain patterns in terms of the equilibrium equations governing the balance between the linear and nonlinear forces in the equilibrium state. Further, we develop a method for predicting the phase in the equilibrium state achieved after the dynamical evolution of a system with given initial parameters. The analytically hard third-order term is approximated using the restricted phase-space approximation [Anzaki et al., Ann. Phys. (NY) 353, 107 (2015)] for the Φ~4 models. Although the proposed method does not have perfect concordance with the actual numerical results, it has no arbitrary parameters and functions to tune the prediction. In other words, it is a method with no a priori assumptions of the domain patterns.