Related papers: The Field Theory Approach to Percolation Processes
A quantum field theoretic formulation of the dynamics of the Contact Process on a regular graph of degree z is introduced. A perturbative calculation in powers of 1/z of the effective potential for the density of particles phi(t) and an…
The coupling of branching-annihilating random walks to a static field with a local conservation law is shown to change the scaling properties of their phase transitions to absorbing states. In particular, we find that DP-class transitions…
Hybrid percolation transitions (HPTs) induced by cascading processes have been observed in diverse complex systems such as $k$-core percolation, breakdown on interdependent networks and cooperative epidemic spreading models. Much effort has…
Percolation on two-dimensional small-world networks has been proposed as a model for the spread of plant diseases. In this paper we give an analytic solution of this model using a combination of generating function methods and high-order…
The electromechanical response of polymeric soft matter to applied electric fields is of fundamental scientific interest as well as relevant to technologies for sensing and actuation. Several existing theoretical and numerical approaches…
The pair contact process (PCP) is a nonequilibrium stochastic model which, like the basic contact process (CP), exhibits a phase transition to an absorbing state. The two models belong to the directed percolation (DP) universality class,…
Systems with absorbing (trapped) states may exhibit a nonequilibrium phase transition from a noise-free inactive phase into an ever-lasting active phase. We briefly review the absorbing critical phenomena and universality classes, and…
We discuss the use of field theory for the exact determination of universal properties in two-dimensional statistical mechanics. After a compact derivation of critical exponents of main universality classes, we turn to the off-critical…
Percolation is a concept widely used in many fields of research and refers to the propagation of substances through porous media (e.g., coffee filtering), or the behaviour of complex networks (e.g., spreading of diseases). Percolation…
We develop a field-theoretic description of large-scale structure formation by taking the non-relativistic limit of a canonically transformed, real scalar field which is minimally coupled to scalar gravitational perturbations in…
We discuss attacks and infections at propagating fronts of percolation processes based on the extended general epidemic process. The scaling behavior of the number of the attacked and infected sites in the long time limit at the ordinary…
Using perturbative renormalization group we investigate the influence of random velocity field on the critical behavior of directed bond percolation process near its second-order phase transition between absorbing and active phase.…
With a scalar potential and a bivector potential, the vector field associated with the drift of a diffusion is decomposed into a generalized gradient field, a field perpendicular to the gradient, and a divergence-free field. We give such…
We review the field-theoretic renormalization-group approach to critical properties of flat polymerized membranes. We start with a presentation of the flexural effective model that is entirely expressed in terms of a transverse (flexural)…
Using field-theoretic renormalization group methods we calculate the equation of state for non-equilibrium systems belonging to the universality class of directed percolation (Gribov process) to second order in epsilon = 4-d. By introducing…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…
A general self-consistency approach allows a thorough treatment of the corrections to the standard mean-field approximation (MFA). The natural extension of standard MFA with the help of a cumulant expansion leads to a new point of view on…
The well-established universality classes of absorbing critical phenomena are directed percolation (DP) and directed Ising (DI) classes. Recently, the pair contact process with diffusion (PCPD) has been investigated extensively and claimed…
We generalize the directed percolation (DP) model by relaxing the strict directionality of DP such that propagation can occur in either direction but with anisotropic probabilities. We denote the probabilities as $p_{\downarrow}= p \cdot…
In this talk I will present some of the main difficulties we encounter in studying the large scale behavior of disordered systems. This presentation will be done using a field theory language. The difficulties in applying the standard…