We study the variational limit of the frustrated J(1)-J(2)-J(3) spin model on the square lattice in the vicinity of the ferromagnet/helimagnet transition point as the lattice spacing vanishes. We carry out the Gamma-convergence analysis of proper scalings of the energy and we characterize the optimal cost of a chirality transition in BV proving that the system is asymptotically driven by a discrete version of a non-linear perturbation of the Aviles-taiga energy functional.
Variational Analysis of the J1-J2-J3 Model: A Non-linear Lattice Version of the Aviles-Giga Functional
Gianluca Orlando
2022-01-01
Abstract
We study the variational limit of the frustrated J(1)-J(2)-J(3) spin model on the square lattice in the vicinity of the ferromagnet/helimagnet transition point as the lattice spacing vanishes. We carry out the Gamma-convergence analysis of proper scalings of the energy and we characterize the optimal cost of a chirality transition in BV proving that the system is asymptotically driven by a discrete version of a non-linear perturbation of the Aviles-taiga energy functional.File in questo prodotto:
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