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

@article{Cicalese2021CoarseGA,
title={Coarse graining and large-\$N\$ behavior of the \$d\$-dimensional \$N\$-clock model},
author={Marco Cicalese and Gianluca Orlando and Matthias Ruf},
journal={Interfaces and Free Boundaries},
year={2021}
}
• Published 5 April 2020
• Mathematics
• Interfaces and Free Boundaries
We study the asymptotic behavior of the $N$-clock model, a nearest neighbors ferromagnetic spin model on the $d$-dimensional cubic $\varepsilon$-lattice in which the spin field is constrained to take values in a discretization $\mathcal{S}_N$ of the unit circle~$\mathbb{S}^{1}$ consisting of $N$ equispaced points. Our $\Gamma$-convergence analysis consists of two steps: we first fix $N$ and let the lattice spacing $\varepsilon \to 0$, obtaining an interface energy in the continuum defined on…
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