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Chirality transitions in frustrated S2-valued spin systems

    https://doi.org/10.1142/S0218202516500366Cited by:7 (Source: Crossref)

    We study the discrete-to-continuum limit of the helical XY S2-spin system on the lattice 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 S1-model presents scalar chirality transitions, the cost of every vectorial chirality transition is zero. In addition we show that if the energy of the system is modified penalizing the distance of the S2-field from a finite number of copies of S1, it is still possible to prove the emergence of nontrivial (possibly trace-dependent) chirality transitions.

    Communicated by G. Dal Maso

    AMSC: 49J45, 49M25, 82B20, 82B24

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