Related papers: On directed interacting animals and directed perco…
The directed bond percolation process is studied in the presence of com- pressible velocity fluctuations with long-range correlations. We discuss a construction of a field theoretic action and a way of obtaining its large scale properties…
We present a comprehensive and versatile theoretical framework to study site and bond percolation on clustered and correlated random graphs. Our contribution can be summarized in three main points. (i) We introduce a set of iterative…
We study the emergence of a giant component in a spatial network where the distribution of the metric distances between the nodes is scale-invariant, and the interaction between the nodes has a long-range power-law behavior. The nodes are…
We consider the scaling behavior of directed percolation and of the pair contact process with a conjugated field. In particular we determine numerically the equation of state and show that both models are characterized by the same universal…
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…
The thermal-to-percolative crossover exponent \phi, well-known for ferromagnetic systems, is studied extensively for Edwards-Anderson spin glasses. The scaling of defect energies are determined at the bond percolation threshold p_c, using…
We consider directed percolation with an absorbing boundary in 1+1 and 2+1 dimensions. The distribution of cluster lifetimes and sizes depend on the boundary. The new scaling exponents can be related to the exponents characterizing standard…
Stochastic, spatially extended models for predator-prey interaction display spatio-temporal structures that are not captured by the Lotka-Volterra mean-field rate equations. These spreading activity fronts reflect persistent correlations…
We study a (1+1)-dimensional directed polymer in a random environment on the integer lattice with log-gamma distributed weights. Among directed polymers, this model is special in the same way as the last-passage percolation model with…
Shape-dependent universal crossing probabilities are studied, via Monte Carlo simulations, for bond and site directed percolation on the square lattice in the diagonal direction, at the percolation threshold. Since the system is strongly…
The site and bond percolation problems are conventionally studied on (hyper)cubic lattices, which afford straightforward numerical treatments. The recent implementation of efficient simulation algorithms for high-dimensional systems now…
In this paper, we investigate a model for a $1+1$ dimensional self-interacting and partially directed self-avoiding walk, usually referred to by the acronym IPDSAW. The interaction intensity and the free energy of the system are denoted by…
We analyze a series of interacting Majorana Fermion chains with finite range pair interactions with coupling strength $g$ that all exhibit a tri-critical point that separates an Ising critical phase from a supersymmetric gapped phase. We…
The transition from a microscopic model for the movement of many particles to a macroscopic continuum model for a density flow is studied. The microscopic model for the free flow is completely deterministic, described by an interaction…
We report analytical and numerical modelling of active elastic networks, motivated by experiments on crosslinked actin networks contracted by myosin motors. Within a broad range of parameters, the motor-driven collapse of active elastic…
The width W of the active region around an active moving wall in a directed percolation process diverges at the percolation threshold p_c as W \simeq A \epsilon^{-\nu_\parallel} \ln(\epsilon_0/\epsilon), with \epsilon=p_c-p, \epsilon_0 a…
A monomer-dimer reaction lattice model with lateral repulsion among the same species is studied using a mean-field analysis and Monte Carlo simulations. For weak repulsions, the model exhibits a first-order irreversible phase transition…
Absorbing phase transition in restricted exclusion processes are characterized by simple integer exponents. We show that this critical behaviour flows to the directed percolation (DP) universality class when particle conservation is broken…
We introduce a method for translating any upper bound on the percolation threshold of a lattice $G$ into a lower bound on the exponential growth rate $a(G)$ of lattice animals and vice-versa. We exploit this in both directions. We improve…
The nature of the phase transition in a system of self-propelling particles has been extensively studied during the last few decades. A theoretical model was proposed by T. Vicsek, {\it et. al.} [Phys. Rev. Lett. {\bf 75}, 1226 (1995)] with…