Related papers: Beyond Mean Field: Fluctuation Diagnostics and Fix…
Nonrenormalizable quantum field theories require counterterms; and based on the hard-core interpretation of such interactions, it is initially argued, contrary to the standard view, that counterterms suggested by renormalized perturbation…
In recent years considerable portion of the computer science community has focused its attention on understanding living cell biochemistry and efforts to understand such complication reaction environment have spread over wide front, ranging…
The violent relaxation and the metastable states of the Hamiltonian Mean-Field model, a paradigmatic system of long-range interactions, is studied using a Hamiltonian formalism. Rigorous results are derived algebraically for the time…
Disordered systems are interesting for many physical reasons. In this article, we study the renormalization group property of quenched disorder systems in the presence of a boundary. We construct examples of scalar field theories in various…
We present a unified dynamical mean-field theory for stochastic self-organized critical models. We use a single site approximation and we include the details of different models by using effective parameters and constraints. We identify the…
We propose a mean-field model for describing the averaged properties of a class of stochastic diffusion-limited growth systems. We then show that this model exhibits a morphology transition from a dense-branching structure with a convex…
The mean-field theory for lossy nonlinear composites, described by complex and field-dependent dielectric functions, is presented. By using the spectral representation of linear composites with identical microstructure, we develop…
First-order phase transitions in many-fermion systems are not detected in the susceptibility analysis of common renormalization-group (RG) approaches. Here we introduce a counterterm technique within the functional renormalization-group…
We show by a detailed study of the mean-field approximation, the Gaussian approximation, the perturbation expansion, and the field-theoretic renormalization-group analysis of a $\varphi^{3}$ theory that its instability fixed points with…
Some renormalization group approaches have been proposed during the last few years which are close in spirit to the Nightingale phenomenological procedure. In essence, by exploiting the finite size scaling hypothesis, the approximate…
The flow equations of the renormalisation group permit to analyse the perturbative $n$-point functions of renormalisable quantum field theories. Rigorous bounds implying renormalisablility allow to control large momentum behaviour, infrared…
A cellular automaton model is presented for random walkers with biologically motivated interactions favoring local alignment and leading to collective motion or swarming behavior. The degree of alignment is controlled by a sensitivity…
Non-equilibrium dynamics are present in many aspects of our lives, ranging from microscopic physical systems to the functioning of the brain. What characterizes stochastic models of non-equilibrium processes is the breaking of the…
We propose a method to describe the short-distance behavior of an interface fluctuating in the presence of the wedge-shaped substrate near the critical filling transition. Two different length scales determined by the average height of the…
Kinetic Ising models are powerful tools for studying the non-equilibrium dynamics of complex systems. As their behavior is not tractable for large networks, many mean-field methods have been proposed for their analysis, each based on unique…
Strong, correlated noise in recurrent neural circuits often passes through nonlinear transfer functions, complicating dynamical mean-field analyses of complex phenomena such as transients and bifurcations. We introduce a method that…
As in the preceding paper we aim at identifying the effective theory that describes the fluctuations of the local overlap with an equilibrium reference configuration close to a putative thermodynamic glass transition. We focus here on the…
Using the technique of mean field theory applied to the lattice boundary Ising and tricritical Ising models we provide a qualitative description of their boundary phase diagrams. We will show this is in agreement with the known picture from…
Functional conjugation methods are used to analyze the global structure of various renormalization group trajectories, and to gain insight into the interplay between continuous and discrete rescaling. With minimal assumptions, the methods…
In the present note, a summary of selected aspects of time-dependent mean-field theory is first recalled. This approach is optimized to describe one-body degrees of freedom. A special focus is made on how this microscopic theory can be…