As a continuation of our previously published work, we propose a theoretical framework for the determination of steady-state kinetics in a spin-1 Ising model by the path probability method. The framework is based on the principles of non-equilibrium statistical physics and is quite different from the phenomenological approach. We construct a set of linear kinetic equations for the order parameters using the non-linear dynamic (or rate) equations in the presence of external magnetic field. From the steady-state solutions of the linear equations, an expression for the complex (or dynamic) magnetic susceptibility [Formula: see text] is derived. The temperature dependence of the magnetic dispersion relation [Formula: see text] and magnetic absorption factor [Formula: see text] has been studied in the ferromagnetic (FM) and paramagnetic (PM) phases as well as near the critical regime.

中文翻译：

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使用路径概率法确定自旋 1 Ising 模型中的稳态动力学

作为我们先前发表的工作的延续，我们提出了一个理论框架，用于通过路径概率方法确定自旋 1 Ising 模型中的稳态动力学。该框架基于非平衡统计物理学原理，与现象学方法有很大不同。在存在外部磁场的情况下，我们使用非线性动态（或速率）方程为阶参数构建了一组线性动力学方程。从线性方程的稳态解，导出了复杂（或动态）磁化率[公式：见正文]的表达式。磁色散关系[公式：见正文]和磁吸收因子[公式：