Calculus of Variations and Geometric Measure Theory
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G. Scilla - V. Vallocchia

Chirality transitions in frustrated ferromagnetic spin chains: a link with the gradient theory of phase transitions

created by scilla on 03 Sep 2016
modified on 23 Jul 2018


Published Paper

Inserted: 3 sep 2016
Last Updated: 23 jul 2018

Journal: Journal of Elasticity
Volume: 132
Number: 2
Pages: 271-293
Year: 2018
Doi: 10.1007/s10659-017-9668-8

ArXiv: 1612.07262 PDF


We study chirality transitions in frustrated ferromagnetic spin chains, in view of a possible connection with the theory of Liquid Crystals. A variational approach to the study of these systems has been recently proposed by Cicalese and Solombrino, focusing close to the helimagnet-ferromagnet transition point corresponding to the critical value of the frustration parameter $\alpha=4$. We reformulate this problem for any $\alpha\geq0$ in the framework of surface energies in nonconvex discrete systems with nearest neighbors ferromagnetic and next-to-nearest neighbors antiferromagnetic interactions and we link it to the gradient theory of phase transitions, by showing a uniform equivalence by $\Gamma\hbox{-}$convergence on $[0,4]$ with Modica-Mortola type functionals.

Keywords: $\Gamma\hbox{-}$convergence, Equivalence, Frustrated lattice systems, Chirality transitions, Modica-Mortola


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