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Preprints, Working Papers, ... Year : 2019

Logarithmic variance for the height function of square-ice

Abstract

In this article, we prove that the height function associated with the square-ice model (i.e.~the six-vertex model with $a=b=c=1$ on the square lattice), or, equivalently, of the uniform random homomorphisms from $\mathbb Z^2$ to $\mathbb Z$, has logarithmic variance. This establishes a strong form of roughness of this height function.

Dates and versions

hal-02378647 , version 1 (25-11-2019)

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Hugo Duminil-Copin, Matan Harel, Benoît Laslier, Aran Raoufi, Gourab Ray. Logarithmic variance for the height function of square-ice. 2019. ⟨hal-02378647⟩
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