From discrete to continuum in the helical XY-model: emergence of chirality transitions in the S¹ to S² limit

2024/12/20 by Marco Cicalese, Cicalese, Marco, Dario Reggiani +3
Physics and Astronomy · #Quantum chaos and dynamical systems #Theoretical and Computational Physics #Black Holes and Theoretical Physics

paper · pdf · doi:10.48550/arxiv.2412.15994

Abstract

We analyze the discrete-to-continuum limit of a frustrated ferromagnetic/anti-ferromagnetic \mathbbS²-valued spin system on the lattice λ_nℤ² as λ_n→ 0. For \mathbbS² spin systems close to the Landau-Lifschitz point (where the helimagnetic/ferromagnetic transition occurs), it is well established that for chirality transitions emerge with vanishing energy. Inspired by recent work on the N-clock model, we consider a spin model where spins are constrained to k_n copies of \mathbbS¹ covering \mathbbS² as n→∞. We identify a critical energy-scaling regime and a threshold for the divergence rate of k_n→+∞, below which the Γ-limit of the discrete energies capture chirality transitions while retaining an \mathbbS²-valued energy description in the continuum limit.

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