Calculus of Variations and Geometric Measure Theory

M. Cicalese - M. Ruf - F. Solombrino

Chirality transitions in frustrated $S^{2}$-valued spin systems

created by solombrin on 17 Mar 2015
modified on 18 Jun 2016


Published Paper

Inserted: 17 mar 2015
Last Updated: 18 jun 2016

Journal: Mathematical Models and Methods in Applied Sciences
Volume: 26
Number: 08
Pages: 1481-1529
Year: 2016
Doi: 10.1142/S0218202516500366


We study the discrete-to-continuum limit of the helical XY $S^{2}$-spin system on the lattice $\mathbb{Z}^{2}$. 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 $S^{1}$-model presents scalar chirality transitions, the cost of every vectorial chirality transition is now zero. In addition we show that if the energy of the system is modified penalizing the distance of the $S^{2}$ field from a finite number of copies of $S^{1}$, it is still possible to prove the emergence of nontrivial (possibly trace dependent) chirality transitions.