Static ferromagnetic materials: from the microscopic to the mesoscopic scale

TL;DR

This paper establishes a rigorous connection between microscopic spin lattice models and mesoscopic continuum models of static ferromagnetic materials, validating classical descriptions and paving the way for dynamic analysis.

Contribution

It introduces a mathematical framework linking microscopic and mesoscopic models of ferromagnetism using averaging and Gamma-convergence techniques, confirming classical theories.

Findings

Microscopic and mesoscopic models are mathematically connected.

Classical continuous models are justified by rigorous derivation.

Framework sets the stage for dynamic ferromagnetic modeling.

Abstract

Thanks to averaging processes and Gamma-convergence techniques, we are able to link a microscopic description of ferromagnetic materials based on spin lattices and their mesoscopic description in the static framework for the three fundamental contributions: exchange, magnetostatic and external field. The results are in accordance with the classical continuous description of ferromagnetic phenomena and justifies it. This work is a seed towards a dynamic description of ferromagnetic materials.