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

physical review. b./physical review. b

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