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Stochastic ferromagnetism. Analysis and numerics. (English) Zbl 1288.82001
De Gruyter Studies in Mathematics 58. Berlin: de Gruyter (ISBN 978-3-11-030699-6/hbk; 978-3-11-030710-8/ebook). vi, 242 p. (2014).
This is a highly professional monograph on computational procedures of solving equations relevant to dynamical processes involving nanomagnetic structures. In particular, the authors study details of thermally activated magnetization dynamics using the stochastic Landau-Lifshitz-Gilbert equation and its numerical solutions to describe an interacting spin system coupled to the surrounding degrees of freedom. The book contains vi+242 pages of text divided into three chapters followed by the bibliography with 111 most recent entries.
The role of noise in finite ensembles of nanomagnetic particles is treated in Chapter 1. Here, one finds essentials needed to understand the noise in stochastic processes, ergodicity, and numerical schemes for solving the stochastic Landau-Lifshitz-Gilbert equation. Chapter 2 is focused on mathematical and numerical details of the procedure of solving the stochastic Landau-Lifshitz-Gilbert equation. This includes the random walk method, properties of numerical discretization, and convergence and stability of solutions. The last Chapter 3 deals with the effective macroscopic deterministic equation describing temperature effects on macro-spin, and compares numerical treatments for the macroscopic model and stochastic approach.

MSC:
82-02 Research exposition (monographs, survey articles) pertaining to statistical mechanics
82-08 Computational methods (statistical mechanics) (MSC2010)
78-02 Research exposition (monographs, survey articles) pertaining to optics and electromagnetic theory
82D40 Statistical mechanics of magnetic materials
82D80 Statistical mechanics of nanostructures and nanoparticles
82B26 Phase transitions (general) in equilibrium statistical mechanics
82B31 Stochastic methods applied to problems in equilibrium statistical mechanics
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