Related papers: Mean-field theory is exact for the random-field mo…
The fact that mean field theory is appropriate to describe an Ising model with long-range interactions has been already shown by Cannas and Tamarit. Although not explicited in our Letter, we have used periodic boundary conditions in all our…
We present a non-perturbative, mean-field theory for the Fermi-Pasta-Ulam-Tsingou model with quartic interaction, capturing the quasiperiodic features shown by the system at all energies in the thermodynamic limit. Starting from the true…
The mean field approximation to the Ising model is a canonical variational tool that is used for analysis and inference in Ising models. We provide a simple and optimal bound for the KL error of the mean field approximation for Ising models…
In quantum field theory there is now a well developed technique, effective field theory, which allows one to obtain low energy quantum predictions in ``non-renormalizable'' theories, using only the degrees of freedom and interactions…
In this work, we present an effective field theory to describe a two-component Fermi gas near a $d$-wave interaction resonance. The effective field theory is renormalizable by matching with the low energy $d$-wave scattering phase shift.…
Mean field limits are an important tool in the context of large-scale dynamical systems, in particular, when studying multiagent and interacting particle systems. While the continuous-time theory is well-developed, few works have considered…
Recent studies have shown that concepts of effective field theory such as naturalness can be profitably applied to relativistic mean-field models of nuclei. Here the analysis by Friar, Madland, and Lynn of naturalness in a relativistic…
We present a simple strategy in order to show the existence and uniqueness of the infinite volume limit of thermodynamic quantities, for a large class of mean field disordered models, as for example the Sherrington-Kirkpatrick model, and…
We study the problem of parameter estimation for large exchangeable interacting particle systems when a sample of discrete observations from a single particle is known. We propose a novel method based on martingale estimating functions…
Mean-field games have been studied under the assumption of very large number of players. For such large systems, the basic idea consists to approximate large games by a stylized game model with a continuum of players. The approach has been…
Ising model is a widely studied class of models in quantum computation. In this paper we investigate the computational characteristics of the random field Ising model (RFIM) with long-range interactions that decays as an inverse polynomial…
An effective field theory for clean electron systems is developed in analogy to the generalized nonlinear sigma-model for disordered interacting electrons. The physical goal is to separate the soft or massless electronic degrees of freedom…
Independent random monomer activities are considered on a mean-feld monomer-dimer model. Under very general conditions on the randomness the model is shown to have a self-averaging pressure density that obeys a solvable variational…
When spatial correlations are short-range, the physics of strongly correlated systems is controlled by local quantum fluctuations. In those regimes, Dynamical Mean-Field Theory can be viewed as a `compass' which provides guidance on the…
Mean field games are studied by means of the weak formulation of stochastic optimal control. This approach allows the mean field interactions to enter through both state and control processes and take a form which is general enough to…
We derive a theory of superfluidity for a dilute Fermi gas that is valid when scattering resonances are present. The treatment of a resonance in many-body atomic physics requires a novel mean-field approach starting from an unconventional…
The mean-field limit in a weakly interacting stochastic many-particle system for multiple population species in the whole space is proved. The limiting system consists of cross-diffusion equations, modeling the segregation of populations.…
We analyze the equilibrium properties of a chain of ferromagnetically coupled rotators which interact through a force that decays as $r^{-\alpha}$ where r is the interparticle distance and $\alpha\ge 0$. Our model contains as particular…
The zero temperature relaxational dynamics of a particle in a short range correlated random potential is addressed. We derive a set of "two-times" mean-field dynamical equations, accounting for a possible mean displacement of the particle…
Effective field theory is applied to finite-density systems with an unnaturally large scattering length, such as neutron matter. A new organizational scheme is identified and connected with an expansion in inverse powers of the number of…