Related papers: Universality classes for percolation models with l…
We obtain explicit expressions for the long range correlations in the ABC model and in diffusive models conditioned to produce an atypical current of particles.In both cases, the two-point correlation functions allow to detect the…
In this note we study the field theory of dynamic isotropic percolation (DIP) with quenched randomness that has long range correlations decaying as $r^{-a}$. We argue that the quasi static limit of this field theory describes the critical…
We introduce a percolation model on $\mathbb{Z}^d$, $d \geq 3$, in which the discrete lines of vertices that are parallel to the coordinate axis are entirely removed at random and independently of each other. In this way a vertex belongs to…
Statistical mechanical systems at and near their points of phase transition are expected to exhibit rich, fractal-like behaviour that is independent of the small-scale details of the system but depends strongly on the dimension in which the…
This article investigates the effect for random pinning models of long range power-law decaying correlations in the environment. For a particular type of environment based on a renewal construction, we are able to sharply describe the phase…
We define a percolation problem on the basis of spin configurations of the two dimensional XY model. Neighboring spins belong to the same percolation cluster if their orientations differ less than a certain threshold called the conducting…
Despite original claims of a first-order transition in the product rule model proposed by Achlioptas et al. [Science 323, 1453 (2009)], recent studies indicate that this percolation model, in fact, displays a continuous transition. The…
Consider an independent site percolation model with parameter $p \in (0,1)$ on $\Z^d,\ d\geq 2$ where there are only nearest neighbor bonds and long range bonds of length $k$ parallel to each coordinate axis. We show that the percolation…
A general formulation of translationally invariant, parametrically correlated random matrix ensembles, is used to classify universality in correlation functions. Surprisingly, the range of possible physical systems is bounded, and can be…
For ordinary (independent) percolation on a large class of lattices it is well known that below the critical percolation parameter $p_c$ the cluster size distribution has exponential decay and that power-law behavior of this distribution…
We introduce a continuum percolation model defined on the points of a d-dimensional homogeneous Poisson process. Each Poisson point is connected to all points within its connection range, which depends on the distances to the other Poisson…
We consider self-avoiding walk and percolation in $\Zd$, oriented percolation in $\Zd\times\Zp$, and the contact process in $\Zd$, with $p D(\cdot)$ being the coupling function whose range is denoted by $L<\infty$. For percolation, for…
We propose a method of studying the continuous percolation of aligned objects as a limit of a corresponding discrete model. We show that the convergence of a discrete model to its continuous limit is controlled by a power-law dependency…
Many non-equilibrium systems display dynamic phase transitions from active to absorbing states, where fluctuations cease entirely. Based on a field theory representation of the master equation, the critical behavior can be analyzed by means…
We consider near-critical planar systems with boundary conditions inducing phase separation. While order parameter correlations decay exponentially in pure phases, we show by direct field theoretical derivation how phase separation…
We study the history-dependent percolation in two dimensions, which evolves in generations from standard bond-percolation configurations through iteratively removing occupied bonds. Extensive simulations are performed for various…
The two-dimensional site percolation problem is studied by transfer-matrix methods on finite-width strips with free boundary conditions. The relationship between correlation-length amplitudes and critical indices, predicted by conformal…
We consider oriented percolation on Z^d times Z_+ whose bond-occupation probability is pD(...), where p is the percolation parameter and D is a probability distribution on Z^d. Suppose that D(x) decays as |x|^{-d-\alpha} for some \alpha>0.…
In this work we consider the steady state scaling behavior of directed percolation around the upper critical dimension. In particular we determine numerically the order parameter, its fluctuations as well as the susceptibility as a function…
We investigate spatial random graphs defined on the points of a Poisson process in $d$-dimensional space, which combine scale-free degree distributions and long-range effects. Every Poisson point is assigned an independent weight. Given the…