A Phase Prediction Method for Pattern Formation in Time-Dependent Ginzburg-Landau Dynamics for Kinetic Ising Model without a priori Assumptions on Domain Patterns

TL;DR

This paper introduces a parameter-free phase prediction method for magnetic pattern formation in a time-dependent Ginzburg-Landau model of the kinetic Ising system, accounting for material thickness and long-range interactions.

Contribution

It develops a new theoretical framework and a prediction method that does not rely on prior assumptions about domain patterns, using a restricted phase-space approximation.

Findings

The method predicts equilibrium phases with no arbitrary parameters.

It captures the effects of material parameters on domain formation.

The approach offers a new perspective on pattern prediction in magnetic systems.

Abstract

We propose a phase prediction method for the pattern formation in the uniaxial two-dimensional kinetic Ising model with the dipole-dipole interactions under the time-dependent Ginzburg-Landau dynamics. Taking the effects of the material thickness into account by assuming the uniformness along the magnetization axis, the model corresponds to thin magnetic materials with long-range repulsive interactions. We propose a new theoretical basis to understand the effects of the material parameters on the formation of the magnetic domain patterns in terms of the equation of balance governing the balance between the linear- and nonlinear forces in the equilibrium state. Based on this theoretical basis, we propose a new method to predict the phase in the equilibrium state reached after the time-evolution under the dynamics with a given set of parameters, by approximating the third-order term using the restricted phase-space approximation [R. Anzaki, K. Fukushima, Y. Hidaka, and T. Oka, Ann. Phys. 353, 107 (2015)] for the $\phi^4$-models. Although the proposed method does not have the 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 on domain patterns.