Related papers: Rigidity of the interface for percolation and rand…
We develop a full theoretical approach to clustering in complex networks. A key concept is introduced, the edge multiplicity, that measures the number of triangles passing through an edge. This quantity extends the clustering coefficient in…
We study the percolation properties of geometrical clusters defined in the overlap space of two statistically independent replicas of a square-lattice Ising model that are simulated at the same temperature. In particular, we consider two…
To investigate order-order interfaces, we perform multimagnetical Monte Carlo simulations of the $2D$ and $3D$ Ising model. Following Binder we extract the interfacial free energy from the infinite volume limit of the magnetic probability…
The generalization of Kasteleyn and Fortuin clusters formalism is introduced in XY (or more generally O(n)) models. Clusters geometrical structure may be linked to spin physical properties as correlation functions. To investigate…
We consider the equilibrium statistical properties of interfaces submitted to competing interactions; a long-range repulsive Coulomb interaction inherent to the charged interface and a short-range, anisotropic, attractive one due to either…
Making use of a recent complete calculation of a chiral six-point correlation function C(z) in a rectangle we calculate various quantities of interest for percolation (SLE parameter \kappa = 6) and many other two-dimensional critical…
Standard statistical mechanical or condensed matter arguments tell us that bulk properties of a physical system do not depend too much on boundary conditions. Random tilings of large regions provide counterexamples to such intuition, as…
Density profiles are investigated arising in a critical Ising model in two dimensions which is confined to a rectangular domain with uniform or mixed boundary conditions and arbitrary aspect ratio. For the cases in which the two vertical…
A one-dimensional interacting particle system is said to exhibit interface tightness if starting in an initial condition describing the interface between two constant configurations of different types, the process modulo translations is…
The class of random-cluster models is a unification of a variety of stochastic processes of significance for probability and statistical physics, including percolation, Ising, and Potts models; in addition, their study has impact on the…
The dynamics of a driven interface in a medium with random pinning forces is analyzed. The interface undergoes a depinning transition where the order parameter is the interface velocity $v$, which increases as $v \sim (F-F_c)^\theta$ for…
The critical behaviour of many spin models can be equivalently formulated as percolation of specific site-bond clusters. In the presence of an external magnetic field, such clusters remain well-defined and lead to a percolation transition,…
Herein, we propose a site random cluster model by introducing an additional cluster weight in the partition function of the traditional site percolation. To simulate the model on a square lattice, we combine the color-assignation and the…
We provide deterministic controllability conditions that imply exponential mixing properties for randomly forced constrained dynamical systems with possibly unbounded state space. As an application, new ergodicity results are obtained for…
We consider a system of particles undergoing correlated diffusion with elastic boundary conditions on the half-line. By taking the large particle limit we establish existence and uniqueness for the limiting empirical measure valued process…
We consider three-dimensional statistical systems at phase coexistence in the half-volume with boundary conditions leading to the presence of an interface. Working slightly below the critical temperature, where universal properties emerge,…
We consider the density of two-dimensional critical percolation clusters, constrained to touch one or both boundaries, in infinite strips, half-infinite strips, and squares, as well as several related quantities for the infinite strip. Our…
This article is devoted to the study of a finite system of long clusters of subcritical 2-dimensional FK-percolation with q $\geq$ 1, conditioned on mutual avoidance. We show that the diffusive scaling limit of such a system is given by a…
We study versions of the contact process with three states, and with infections occurring at a rate depending on the overall infection density. Motivated by a model described in [17] for vegetation patterns in arid landscapes, we focus on…
Global physical properties of random media change qualitatively at a percolation threshold, where isolated clusters merge to form one infinite connected component. The precise knowledge of percolation thresholds is thus of paramount…