Percolation models describe the inside of a porous material. The theory emerged timidly in
the middle of the twentieth century before becoming one of the major objects of interest in …

The effect of decoherence on topological order (TO) has been most deeply understood for
the toric code, the paragon of Abelian TOs. We show that certain non-Abelian TOs can be …

We show that the height function of the six-vertex model, in the parameter range a D b D 1
and c 1, is delocalized with logarithmic variance when c Ä 2. This complements the earlier …

This paper is studying the critical regime of the planar random-cluster model on Z 2 with
cluster-weight q∈[1, 4). More precisely, we prove crossing estimates in quads which are …

The interest is in models of integer-valued height functions on shift-invariant planar graphs
whose maximum degree is three. We prove delocalisation for models induced by convex …

The classical spin O (n) model is a model on ad-dimensional lattice in which a vector on the
(n-1)-dimensional sphere is assigned to every lattice site and the vectors at adjacent sites …

Graph homomorphisms from the Z^ d Z d lattice to ZZ are functions on Z^ d Z d whose
gradients equal one in absolute value. These functions are the height functions …

In this article, we prove that the height function associated with the square-ice model (ie the
six-vertex model with a= b= c= 1 on the square lattice), or, equivalently, of the uniform …

We consider a general system of interacting random loops which includes several models of
interest, such as the Spin O (N) model, random lattice permutations, a version of the …

We prove a general Russo–Seymour–Welsh (RSW) result valid for any invariant bond
percolation measure on Z 2 satisfying positive association. This means that the crossing …