Related papers: Mean Field Behaviour in a Local Low-Dimensional Mo…
We investigate an $N$-particle Bose-Hubbard dimer with an additional effective decay term in one of the sites. A mean-field approximation for this non-Hermitian many-particle system is derived, based on a coherent state approximation. The…
We use scaling results to identify the crossover to mean-field behavior of equilibrium statistical mechanics models on a variant of the small world network. The results are generalizable to a wide-range of equilibrium systems. Anomalous…
We review and refine the concept of a mean-field theory for the study of sandpile models, which are of central importance in the study of self-organized criticality. By considering the simple one-dimensional random walker with an absorbing…
We study the phase diagram and critical behavior of an interacting one dimensional two species monomer-monomer catalytic surface reaction model with a reactive phase as well as two equivalent adsorbing phase where one of the species…
We study the spin-1/2 Ising model on a Bethe lattice in the mean-field limit, with the interaction constants following two deterministic aperiodic sequences: Fibonacci or period-doubling ones. New algorithms of sequence generation were…
Second-order phase transitions appear as a divergence in one of the linear response functions. For a system of correlated electrons, the relevant divergent response can and does involve many-particle observables, most famously the double…
Dynamical mean-field approximations are performed to study the phase transition of a pair contact process with diffusion in different spatial dimensions. The level of approximation is extended up to 18-site clusters for the one-dimensional…
This paper studies a general class of stochastic population processes in which agents interact with one another over a network. Agents update their behaviors in a random and decentralized manner according to a policy that depends only on…
We propose a mean-field (MF) approximation for the recurrence relation governing the dynamics of $m$ species of particles on a square lattice, and we simultaneously perform Monte Carlo (MC) simulations under identical initial conditions to…
Phase transitions of reaction-diffusion systems with site occupation restriction and with particle creation that requires n>1 parents and where explicit diffusion of single particles (A) exists are reviewed. Arguments based on mean-field…
Mean-field approximation is often used to explore the qualitative behaviour of phase transitions in classical spin models before employing computationally costly methods such as the Monte-Carlo techniques. We implement a 'lattice…
This article proposes a new way of deriving mean-field exponents for the weakly self-avoiding walk model in dimensions $d>4$. Among other results, we obtain up-to-constant estimates for the full-space and half-space two-point functions in…
The $q=2$ random cluster model is studied in the context of two mean field models: The Bethe lattice and the complete graph. For these systems, the critical exponents that are defined in terms of finite clusters have some anomalous values…
Bootstrap, or $k$-core, percolation displays on the Bethe lattice a mixed first/second order phase transition with both a discontinuous order parameter and diverging critical fluctuations. I apply the recently introduced $M$-layer technique…
We introduce a mean-field model of lattice trees based on embeddings into $\Z^d$ of abstract trees having a critical Poisson offspring distribution. This model provides a combinatorial interpretation for the self-consistent mean-field model…
We present a unified mean-field theory, based on the single site approximation to the master-equation, for stochastic self-organized critical models. In particular, we analyze in detail the properties of sandpile and forest-fire (FF)…
Mean-Field is an efficient way to approximate a posterior distribution in complex graphical models and constitutes the most popular class of Bayesian variational approximation methods. In most applications, the mean field distribution…
This paper investigates the use of transformers to approximate the mean-field dynamics of interacting particle systems exhibiting collective behavior. Such systems are fundamental in modeling phenomena across physics, biology, and…
Many complex dynamical systems in the real world, including ecological, climate, financial, and power-grid systems, often show critical transitions, or tipping points, in which the system's dynamics suddenly transit into a qualitatively…
Many non-equilibrium processes on scale-free networks present anomalous critical behavior that is not explained by standard mean-field theories. We propose a systematic method to derive stochastic equations for mean-field order parameters…