Coarse graining and large- behavior of the -dimensional -clock model
Marco Cicalese
Technische Universität München, Garching, GermanyGianluca Orlando
Politecnico di Bari, ItalyMatthias Ruf
Ecole Polytechnique Fédérale de Lausanne, Switzerland
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Abstract
We study the asymptotic behavior of the -clock model, a nearest neighbors ferromagnetic spin model on the -dimensional cubic -lattice in which the spin field is constrained to take values in a discretization of the unit circle consisting of equispaced points. Our -convergence analysis consists of two steps: we first fix and let the lattice spacing , obtaining an interface energy in the continuum defined on piecewise constant spin fields with values in ; at a second stage, we let . The final result of this two-step limit process is an anisotropic total variation of -valued vector fields of bounded variation.
Cite this article
Marco Cicalese, Gianluca Orlando, Matthias Ruf, Coarse graining and large- behavior of the -dimensional -clock model. Interfaces Free Bound. 23 (2021), no. 3, pp. 323–351
DOI 10.4171/IFB/456