Coarse graining in micromagnetics

The problem of overestimated Curie temperatures is solved by an appeal to the low-temperature renormalization of fixed-length spin models. The main point is that the effective exchange constant of the coarse-grained system experiences a temperature-dependent renormalization, thus producing a phase transition at the proper temperature. Furthermore, it is demonstrated that even at temperatures far below criticality, magnetic properties computed numerically from the LLG equations depend on block size.