Two geometric lemmas for $S^{N-1}$-valued maps and an application to the homogenization of spin systems

Andrea Braides; Valerio Vallocchia

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arXiv · 2010.14280

Two geometric lemmas for $S^{N-1}$-valued maps and an application to the homogenization of spin systems

Andrea Braides·Valerio Vallocchia

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Abstract

We prove two geometric lemmas for $S^{N-1}$-valued functions that allow to modify sequences of lattice spin functions on a small percentage of nodes during a discrete-to-continuum process so as to have a fixed average. This is used to simplify known formulas for the homogenization of spin systems.

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Andrea Braides, Valerio Vallocchia. 2020-10-27. Two geometric lemmas for $S^{N-1}$-valued maps and an application to the homogenization of spin systems. https://arxiv.org/abs/2010.14280

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