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

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 ${\varphi }^4$-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.

References in corpus (5)

• Theory of domain patterns in systems with long-range interactions of Coulomb type
• Numerical simulations of two dimensional magnetic domain patterns
• Field sweep rate dependence of magnetic domain patterns: Numerical simulations for a simple Ising-like model
• Magnetic Domain Patterns Depending on the Sweeping Rate of Magnetic Fields
• Restricted phase-space approximation in real-time stochastic quantization

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