Logarithmic variance for the height function of square-ice

Thursday, 31 October, 2019

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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.


Hugo Duminil-Copin
Matan Harel
Benoit Laslier
Aran Raoufi
Gourab Ray