Volume 27, 2021
Special issue in the honor of Enrique Zuazua's 60th birthday
|Number of page(s)||13|
|Published online||11 March 2021|
Two geometric lemmas for 𝒮N−1-valued maps and an application to the homogenization of spin systems*,
Dipartimento di Matematica Università di Roma “Tor Vergata”,
via della ricerca scientifica 1,
** Corresponding author: firstname.lastname@example.org
Accepted: 9 January 2021
We prove two geometric lemmas for 𝒮N−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.
Mathematics Subject Classification: 35B27 / 74Q05 / 49J45
Key words: Spin systems / maps with values on the sphere / lattice energies / discrete-to-continuum / homogenization
© EDP Sciences, SMAI 2021
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