Chirality transitions in frustrated S2-valued spin systems

Chirality Transitions in Frustrated S2 -valued Spin Systems

We study the discrete-to-continuum limit of the helical XY S -spin system on the lattice Z . We scale the interaction parameters in order to reduce the model to a spin chain in the vicinity of the Landau-Lifschitz point and we prove that at the same energy scaling under which the S -model presents scalar chirality transitions, the cost of every vectorial chirality transition is now zero. In add...

Frustrated Ferromagnetic Spin Chains: A Variational Approach to Chirality Transitions

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 Γ-limits of proper renormalizations and scalings, the energy...

First-Order Phase Transitions in Frustrated Spin Systems

We give a short review of our recent works on the first-order quantum phase transitions in frustrated spin chains with orthogonal-dimer structure. When the ratio of the competing antiferromagnetic exchange couplings is varied, a first-order transition occurs between the dimer phase and the plaquette phase, which is accompanied by the discontinuity in the spin excitation gap. We further show tha...

Spin and Chirality Orderings of Frustrated Magnets — Stacked-Triangular Antiferromagnets and Spin Glasses

“Chirality” is a multispin quantity representing the sense or the handedness of the noncollinear spin structures induced by spin frustration. Recent studies have revealed that the chirality often plays an important role in the ordering of certain frustrated magnets. Here I take up two such examples, stacked-triangular antiferromagnets and spin glasses, where the inherent chiral degree of freedo...

Variational approach for uniformly frustrated 2D XY spin systems. I. Phase transitions in modulated arrays