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Abstract

 The Landau–Lifshitz–Bloch (LLB) equation is a pivotal mathematical framework for modeling magnetization dynamics at elevated temperatures, especially near the Curie point. Its ability to account for both longitudinal and transverse relaxation effects makes it highly relevant for investigating ultrafast magnetization processes. This paper explores the stability characteristics of the LLB equation under various physical and numerical conditions, with a focus on its behavior in deterministic and stochastic regimes. Through analytical derivations and computational simulations, we identify key factors influencing stability, such as temperature dependence, damping parameters, and external magnetic fields. Our findings contribute to the development of robust numerical schemes and improved understanding of magnetization dynamics in high-temperature regimes, with implications for magnetic recording technologies and spintronic applications.

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Review