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

Abstract

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 $\alpha \ge 0$ 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 $\Gamma$-convergence on $[0,4]$ with Modica-Mortola type functionals.

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