Frustrated ferromagnetic spin chains: a variational approach to chirality transitions

TL;DR

This paper investigates the energy behavior and chirality transitions in a one-dimensional frustrated spin chain near the helimagnet/ferromagnet transition, using a variational approach and Gamma-convergence techniques.

Contribution

It provides a rigorous analysis of chiral ground states and computes the energy for chirality transitions in frustrated spin chains.

Findings

Emergence of chiral ground states near transition point

Explicit energy calculations for chirality transitions

Application of Gamma-convergence to spin chain energy analysis

Abstract

We study the energy per particle of a one-dimensional ferromagnetic/anti-ferromagnetic frustrated spin chain with nearest and next-to-nearest interactions close to the helimagnet/ferromagnet transition point as the number of particles diverges. We rigorously prove the emergence of chiral ground states and we compute, by performing the Gamma-limits of proper renormalizations and scalings, the energy for a chirality transition.