Delocalization of Uniform Graph Homomorphisms from Z2 to Z
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220_2021_4181_ReferencePDF.pdf
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Author(s)
Chandgotia, Nishant
Peled, Ron
Sheffield, Scott
Tassy, Martin
Date Issued
September 13, 2021
Publisher
Springer Berlin Heidelberg
Citation
Chandgotia, Nishant, Peled, Ron, Sheffield, Scott and Tassy, Martin. 2021. "Delocalization of Uniform Graph Homomorphisms from Z2 to Z."
Version
Author's final manuscript
Abstract
Abstract
Graph homomorphisms from the
$${\mathbb {Z}}^d$$
Z
d
lattice to
$${\mathbb {Z}}$$
Z
are functions on
$${\mathbb {Z}}^d$$
Z
d
whose gradients equal one in absolute value. These functions are the height functions corresponding to proper 3-colorings of
$${\mathbb {Z}}^d$$
Z
d
and, in two dimensions, corresponding to the 6-vertex model (square ice). We consider the uniform model, obtained by sampling uniformly such a graph homomorphism subject to boundary conditions. Our main result is that the model delocalizes in two dimensions, having no translation-invariant Gibbs measures. Additional results are obtained in higher dimensions and include the fact that every Gibbs measure which is ergodic under even translations is extremal and that these Gibbs measures are stochastically ordered.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/s00220-021-04181-0
