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

TL;DR

This paper investigates chirality transitions in frustrated ferromagnetic spin chains, establishing a connection with the gradient theory of phase transitions through a unified variational framework.

Contribution

It reformulates the problem for all frustration parameters and links it to the gradient theory of phase transitions via $ ext{Gamma}$-convergence, extending previous work near the critical point.

Findings

Established a uniform $ ext{Gamma}$-convergence with Modica-Mortola functionals for all $ ext{alpha}\geq0$

Linked discrete spin chain models to continuum phase transition theories

Extended the variational approach to a broader parameter range

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 $\alpha\geq0$ 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 $\Gamma$-convergence on $[0,4]$ with Modica-Mortola type functionals.