Stochastic ferromagnetism. Analysis and numerics (Q388757)

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.NEWLINENEWLINEThe 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.