Related papers: The Field Theory Approach to Percolation Processes
We introduce a family of classical stochastic processes describing diffusive particles undergoing branching and long-range annihilation in the presence of a parity constraint. The probability for a pair-annihilation event decays as a…
The spreading of infectious diseases with and without immunization of individuals can be modeled by stochastic processes that exhibit a transition between an active phase of epidemic spreading and an absorbing phase, where the disease dies…
Percolation theory dictates an intuitive picture depicting correlated regions in complex systems as densely connected clusters. While this picture might be adequate at small scales and apart from criticality, we show that highly correlated…
This short review covers a wide selection of topics from a multidisciplinary area of dynamics of nonequilibrium systems in physics, chemistry, biology. Theoretical models of colloid particle and protein deposition and adhesion at surfaces,…
The one-dimensional pair contact process with diffusion (PCPD), an interacting particle system with diffusion, pair annihilation, and creation by pairs, has defied a consensus about the universality class that it belongs to. An argument by…
I use a previously introduced mapping between the continuum percolation model and the Potts fluid to derive a mean field theory of continuum percolation systems. This is done by introducing a new variational principle, the basis of which…
The massive field-theory approach for studying critical behavior in fixed space dimensions $d<4$ is extended to systems with surfaces.This enables one to study surface critical behavior directly in dimensions $d<4$ without having to resort…
The stationary state solutions of the Ising-type thin films with different layers in the presence of an external oscillatory field have been examined within the effective field theory. The exhibition focuses on understanding of the external…
A broad class of systems, including ecological, epidemiological, and sociological ones, are characterized by populations of individuals assigned to specific categories, e.g., a chemical species, an opinion or an epidemic state, that are…
Interacting particle systems can often be constructed from a graphical representation, by applying local maps at the times of associated Poisson processes. This leads to a natural coupling of systems started in different initial states. We…
We introduce a correlated static model and investigate a percolation transition. The model is a modification of the static model and is characterized by assortative degree-degree correlation. As one varies the edge density, the network…
The driven transport of plastic systems in various disordered backgrounds is studied within mean field theory. Plasticity is modeled using non-convex interparticle potentials that allow for phase slips. This theory most naturally describes…
The basis for the field theory are properties of the closed exterior differential forms (skew-symmetric differential forms defined on manifolds with the closed metric forms), which reflect properties of the conservation laws for physical…
Mean-field theories of the glass transition predict a phase transition to a dynamically arrested state, yet no such transition is observed in experiments or simulations of finite-dimensional systems. We resolve this long-standing…
A sandpile model with stochastic toppling rule is studied. The control parameters and the phase diagram are determined through a MF approach, the subcritical and critical regions are analyzed. The model is found to have some similarities…
On approaching the dynamical transition temperature, supercooled liquids show heterogeneity over space and time. Static replica theory investigates the dynamical crossover in terms of the free energy landscape (FEL). Two kinds of static…
The field theoretic renormalization group is applied to a simple model of random walk on a rough fluctuating surface. We consider the Fokker--Planck equation for a particle in a uniform gravitational field. The surface is modelled by the…
We develop a unified theory that encompasses the macroscopic dynamics of recurrent interactions of binary units within arbitrary network architectures. Using the martingale theory, our mathematical analysis provides a complete description…
Although real-world complex systems typically interact through sparse and heterogeneous networks, analytic solutions of their dynamics are limited to models with all-to-all interactions. Here, we solve the dynamics of a broad range of…
Mean-field models approximate large stochastic systems by simpler differential equations that are supposed to approximate the mean of the larger system. It is generally assumed that as the stochastic systems get larger (i.e., more people or…