Coarse Graining in Micromagnetics

Numerical solutions of the micromagnetic Landau-Lifshitz-Gilbert equations provide valuable information at low temperatures ([Formula presented]), but produce egregious errors at higher [Formula presented]. For example, Curie temperatures are often overestimated by an order of magnitude. We show that these errors result from the use of block or coarse-grained variables, without a concomitant renormalization of the system parameters to account for the block size. Renormalization solves the problem of the Curie-point anomaly and improves the accuracy of more complicated micromagnetic simulations, even at low [Formula presented]. © 2003 The American Physical Society.