Related papers: Mean-field theory is exact for the random-field mo…
A cluster mean-field method is introduced and the applications to the Ising and Heisenberg models are demonstrated. We divide the lattice sites into clusters whose size and shape are selected so that the equivalence of all sites in a…
A generic feature of systems with long-range interactions is the presence of {\it quasi-stationary} states with non-Gaussian single particle velocity distributions. For the case of the Hamiltonian Mean Field (HMF) model, we demonstrate that…
Incorporating social interactions is essential to an accurate modeling of epidemic spreading. This work proposes a novel local mean-field density functional theory model by using the sum-of-exponential approximation of convolution kernels…
Motivated by considerations from neuroscience (macroscopic behavior of large ensembles of interacting neurons), we consider a population of mean field interacting diffusions in $\mathbf {R}^m$ in the presence of a random environment and…
We use probabilistic methods to study properties of mean-field models, arising as large-scale limits of certain particle systems with mean-field interaction. The underlying particle system is such that $n$ particles move forward on the real…
In this work, we consider general exchangeable quantum mean-field Hamiltonian such as the prominent quantum Curie-Weiss model under the influence of a random external field. Despite being arguably the simplest class of disordered quantum…
A mean field theory of the localization transition for bosonic systems is developed. Localization is shown to be sensitive to the distribution of the random site energies. It occurs in the presence of a triangular distribution, but not a…
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…
Recent work on random field Ising model is described briefly emphasizing exact solutions of the model in simple cases and their relevance in understanding equilibrium and non-equilibrium properties of systems with quenched disorder.
In this work, we explore some interesting details of the time-dependent regime of the long-range systems under mean-field approximation in comparison with the critical dynamics of the short-range systems. First, we discuss some mechanisms…
This article proposes a unified framework to study non-exchangeable mean-field particle systems with some general interaction mechanisms. The starting point is a fixed-point formulation of particle systems originally due to Tanaka that…
Ground-state properties of exotic even-even nuclei with extreme neutron-to-proton ratios are described in the framework of the self-consistent mean-field theory with pairing formulated in coordinate space. This theory properly accounts for…
The mean-field approximation based on effective interactions or density functionals plays a pivotal role in the description of finite quantum many-body systems that are too large to be treated by ab initio methods. Some examples are…
Interacting particle systems are in frequent use to model collective behaviour in various situations and applications. For many systems, the interaction between the agents is restricted to an underlying network structure and often, the…
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…
We investigate a class of quantum field theories with relativistic Luttinger fermions and local self-interaction in scalar channels. For an understanding of possible low-energy phases, we first classify the set of mass terms arising from…
A multi-chain mean-field theory is developed and applied to a two-dimensional system of weakly coupled S=1/2 Heisenberg chains. The environment of a chain C_0 is modeled by a number of neighbor chains C_d, d = +/-1,...,+/-n, with the edge…
Mean-field theory is an approximation replacing an extended system by a few variables. For depinning of elastic manifolds, these are the position of its center of mass $u$, and the statistics of the forces $F(u)$. There are two proposals to…
The method of effective field theories (EFTs) is developed for the scattering of two particles at wavelengths which are large compared to the range of their interaction. It is shown that the renormalized EFT is equivalent to the effective…
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…