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# 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.
Document type :
Preprints, Working Papers, ...
Domain :

https://hal.archives-ouvertes.fr/hal-02378647
Contributor : Benoit Laslier Connect in order to contact the contributor
Submitted on : Monday, November 25, 2019 - 12:10:39 PM
Last modification on : Monday, March 14, 2022 - 4:52:07 PM

### Identifiers

• HAL Id : hal-02378647, version 1
• ARXIV : 1911.00092

### Citation

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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