Variational analysis of a two-dimensional frustrated spin system:\n emergence and rigidity of chirality transitions

2019/04/16 by Marco Cicalese, Cicalese, Marco, Marwin Forster +3 · 1 citation
Physics and Astronomy · Mathematics · #Theoretical and Computational Physics #Mathematical Dynamics and Fractals #Markov Chains and Monte Carlo Methods

paper · pdf · doi:10.48550/arxiv.1904.07792

Abstract

We study the discrete-to-continuum variational limit of the J₁-J₃\nspin model on the square lattice in the vicinity of the helimagnet/ferromagnet\ntransition point as the lattice spacing vanishes. Carrying out the\n\Γ-convergence analysis of proper scalings of the energy, we prove the\nemergence and characterize the geometric rigidity of the chirality phase\ntransitions.\n

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• On the formation of microstructure and the occurrence of vortices in a singularly perturbed energy related to helimagnetism: a scaling law result

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