Coarse graining and large-N behavior of the d-dimensional N-clock model

Marco Cicalese, Gianluca Orlando, Matthias Ruf

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5 Scopus citations


We study the asymptotic behavior of the N -clock model, a nearest neighbors ferromagnetic spin model on the d -dimensional cubic "-lattice in which the spin field is constrained to take values in a discretization SN of the unit circle S1 consisting of N equispaced points. Our г -convergence analysis consists of two steps: we first fix N and let the lattice spacing " ! 0, obtaining an interface energy in the continuum defined on piecewise constant spin fields with values in SN ; at a second stage, we let N ! C1. The final result of this two-step limit process is an anisotropic total variation of S1-valued vector fields of bounded variation.

Original languageEnglish
Pages (from-to)323-351
Number of pages29
JournalInterfaces and Free Boundaries
Issue number3
StatePublished - 2021


  • N -clock model
  • Vector fields of bounded variation with values in the unit circle
  • X Y model
  • г -convergence


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