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

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>0 in the framework of surface energies in nonconvex discrete systems with nearest neighbours ferromagnetic and next-to-nearest neighbours 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.