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We study chirality transitions in frustrated ferromagnetic spin chains, inview of a possible connection with the theory of Liquid Crystals. A variationalapproach to the study of these systems has been recently proposed by Cicaleseand Solombrino, focusing close to the helimagnet-ferromagnet transition pointcorresponding to the critical value of the frustration parameter $\alpha=4$. Wereformulate this problem for any $\alpha\geq0$ in the framework of surfaceenergies in nonconvex discrete systems with nearest neighbors ferromagnetic andnext-to-nearest neighbors antiferromagnetic interactions and we link it to thegradient theory of phase transitions, by showing a uniform equivalence by$\Gamma$-convergence on $[0,4]$ with Modica-Mortola type functionals.

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