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.

36 pages. Substantial revision of the RSW theorem

References in corpus (2)

• A short proof of the discontinuity of phase transition in the planar random-cluster model with $q>4$
• The Bethe ansatz for the six-vertex and XXZ models: an exposition

Cited by in corpus (1)

• From hard spheres to hard-core spins