Geodesic
Coarse graining and large-$N$ behavior of the $d$-dimensional $N$-clock model
Marco Cicalese1 orcid ; Gianluca Orlando2 ; Matthias Ruf3 orcid
1Technische Universität München, Garching, Germany
2Politecnico di Bari, Italy
3Ecole Polytechnique Fédérale de Lausanne, Switzerland
Interfaces and free boundaries, Tome 23 (2021) no. 3, pp. 323-351

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DOI

We study the asymptotic behavior of the N-clock model, a nearest neighbors ferromagnetic spin model on the d-dimensional cubic ε-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 Γ-convergence analysis consists of two steps: we first fix N and let the lattice spacing ε→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→+∞. The final result of this two-step limit process is an anisotropic total variation of S1-valued vector fields of bounded variation.
DOI : 10.4171/ifb/456
Classification : 49-XX, 26-XX, 82-XX
Mots-clés : Γ-convergence, XY model, N-clock model, vector fields of bounded variation with values in the unit circle

Marco Cicalese  1   ; Gianluca Orlando  2   ; Matthias Ruf  3

1 Technische Universität München, Garching, Germany
2 Politecnico di Bari, Italy
3 Ecole Polytechnique Fédérale de Lausanne, Switzerland 
Marco Cicalese; Gianluca Orlando; Matthias Ruf. Coarse graining and large-$N$ behavior of the $d$-dimensional $N$-clock model. Interfaces and free boundaries, Tome 23 (2021) no. 3, pp. 323-351. doi: 10.4171/ifb/456
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     title = {Coarse graining and large-$N$ behavior of the $d$-dimensional $N$-clock model},
     journal = {Interfaces and free boundaries},
     pages = {323--351},
     year = {2021},
     volume = {23},
     number = {3},
     doi = {10.4171/ifb/456},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/456/}
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