## Abstract

We consider a classical Heisenberg system of S^{2} spins on a square lattice of spacing ɛ. We introduce a magnetic anisotropy by constraining the out-of-plane component of each spin to take only finitely many values. Computing the Γ-limit of a suitable scaling of the energy functional as ɛ→0 we prove that, in the continuum description, the system concentrates energy at the boundary of sets in which the out-of-plane component of the spin is constant. In a second step we analyze a different scaling of the energy and we prove that, in each of such phases, the energy can further concentrate on finitely many points corresponding to vortex-like singularities of the in-plane components of the spins.

Original language | English |
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Article number | 112929 |

Journal | Nonlinear Analysis, Theory, Methods and Applications |

Volume | 231 |

DOIs | |

State | Published - Jun 2023 |

## Keywords

- Interface energy
- Topological singularities
- Γ-convergence

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