Percolation is the simplest fundamental model in statistical mechanics that exhibits phase
transitions signaled by the emergence of a giant connected component. Despite its very …

We experimentally investigate the statistics of zero-height isolines in gravity wave turbulence
as physical candidates for conformal invariant curves. We present direct evidence that they …

Using advanced numerical approaches based on optimization algorithms, much progress
has been achieved for the study of the ground-state and low-temperature behavior of two …

Recently, two of us argued that the probability that an FK cluster in the Q-state Potts model
connects three given points is related to the time-like Liouville three-point correlation …

The Ising spin glass in two dimensions exhibits rich behavior with subtle differences in the
scaling for different coupling distributions. We use recently developed mappings to graph …

We show that in the continuum limit watersheds dividing drainage basins are Schramm-
Loewner evolution (SLE) curves, being described by one single parameter κ. Several …

We review two numerical methods related to the Schramm-Loewner evolution (SLE). The
first simulates SLE itself. More generally, it finds the curve in the half-plane that results from …

Amorphous solids may resist external deformation such as shear or compression, while they
do not present any long-range translational order or symmetry at the microscopic scale. Yet …

We have studied the isoheight lines on the WO 3 surface as a physical candidate for
conformally invariant curves. We have shown that these lines are conformally invariant with …

In critical systems, the effect of a localized perturbation affects points that are arbitrarily far
from the perturbation location. In this paper, we study the effect of localized perturbations on …