Related papers: Mean-field theory is exact for the random-field mo…
We derive a mean-field model that is based on a two-component Pauli-like equation and incorporates quantum, spin, and relativistic effects up to second order in $1/c$. Using a Lagrangian approach, we obtain the self-consistent charge and…
We propose an entanglement mean field theory inspired approach for dealing with interacting classical many-body systems. It involves a coarse-graining technique that terminates a step before the mean field theory: While mean field theory…
We derive a rigorous lower bound on the average local energy for the Ising model with quenched randomness. The result is that the lower bound is given by the average local energy calculated in the absence of all interactions other than the…
Mean-field reinforcement learning (MF-RL) scales multi-agent RL to large populations by reducing each agent's dependence on others to a single summary statistic -- the mean action. However, this reduction requires every agent to act at…
The kinetic field theory is developed without assumptions of statistical homogeneity and isotropy. In a solvable toy model with short-ranged interactions, we compare first-order perturbation theory to an iterated mean-field approximation…
In this work, we consider one-dimensional particles interacting in mean-field type through a bounded kernel. In addition, when particles hit some barrier (say zero), they are removed from the system. This absorption of particles is…
A system of fermions with short-range interactions at finite density is studied using the framework of effective field theory. The effective action formalism for fermions with auxiliary fields leads to a loop expansion in which…
We develop theoretical diagnostics for the breakdown of mean-field theory, demonstrate how spatial structure and finite interaction ranges enter the effective description, and show how these scales qualitatively modify the…
We introduce a new class of effective interactions to be used within the energy-density-functional approaches. They are based on regularized zero-range interactions and constitute a consistent application of the effective-theory methodology…
The exact mean-field theory for the simplest glass-forming system - the dense assembly of hard spheres in the large dimensional limit - predicts the existence of a Gardner phase. This transition is characterized by full replica symmetry…
We analyze the mean-field limit of a stochastic Schr{\"o}dinger equation arising in quantum optimal control and mean-field games, where N interacting particles undergo continuous indirect measurement. For the open quantum system described…
This research investigates a novel class of one-dimensional theories characterised by a distinctly defined infinite interaction range. We propose that such theories emerge naturally through a mesoscopic feedback mechanism. In this…
Model Hamiltonians with long-range interaction yield energies that are corrected taking into account the universal behavior of the electron-electron interaction at short range. Although the intention of the paper is to explore the…
A general mean field theory is presented for the construction of equilibrium coarse grained models. Inverse methods that reconstruct microscopic models from low resolution experimental data can be derived as particular implementations of…
We develop an effective field theory to describe the superfluid pairing in strongly interacting fermions with arbitrary short-range attractions, by extending Kaplan's idea of coupling fermions to a fictitious boson state in Nucl. Phys. B…
connected spin-glass models with a discontinuous transition. In the thermodynamic limit the equilibrium properties in the high temperature phase are described by the schematic Mode Coupling Theory of super-cooled liquids. We show that {\it…
We extend a recent billiard model of the nuclear N-body Hamiltonian to consider a finite two-body interaction. This permits a treatment of the Hamiltonian by a mean field theory, and also allows the possibility to model reactions between…
Based on a functional-integral formalism, a generalization of the self-energy-functional theory (SFT) is proposed which is applicable to systems of interacting electrons with disorder. Similar to the pure case without disorder, a…
We introduce a system of self-propelled agents (active Brownian particles) with velocity alignment in two spatial dimensions and derive a mean-field theory from the microscopic dynamics via a nonlinear Fokker-Planck equation and a moment…
The validity of the approximations done in the mean field description of the quasi-elastic excitation of medium-heavy nuclei is discussed. A test of the reliability of the plane wave Born approximation is presented. The uncertainty related…