Related papers: Modified Mean Field approximation for the Ising Mo…
Detailed mean field and Monte Carlo studies of the dynamic magnetization-reversal transition in the Ising model in its ordered phase under a competing external magnetic field of finite duration have been presented here. Approximate…
We develop a transfer matrix method to compute exactly the spin-spin correlation functions of Bethe lattice spin models in the external magnetic field h and for any temperature T. We first compute the correlation function for the most…
In this paper and in the companion one we address the problem of identifying the effective theory that describes the statistics of the fluctuations of what is thought to be the relevant order parameter for glassy systems---the overlap field…
There has been recent progress on the problem of inferring the structure of interactions in complex networks when they are in stationary states satisfying detailed balance, but little has been done for non-equilibrium systems. Here we…
In the present paper we show how non--classical, quite accurate, critical exponents can be extracted in a very simple way from the Pad\'e analysis of the results obtained by mean field like approximation schemes, and in particular by the…
Conformal field theory predicts finite-size scaling amplitudes of correlation lengths universally related to critical exponents on sphere-like, semi-finite systems $S^{d-1}\times\mathbb{R}$ of arbitrary dimensionality $d$. Numerical studies…
An investigation of the spatial fluctuations and their manifestations in the vicinity of the quantum critical point within the framework of the renormalized $\phi^{4}$ theory is proposed. Relevant features are reported through the…
We rederive the finite size scaling formula for the apparent critical temperature by using Mean Field Theory for the Ising Model above the upper critical dimension. We have also performed numerical simulations in five dimensions and our…
This paper proposes a multiscale method for solving the numerical solution of mean field games which accelerates the convergence and addresses the problem of determining the initial guess. Starting from an approximate solution at the…
Integration against a probability distribution given its unnormalized density is a central task in Bayesian inference and other fields. We introduce new methods for approximating such expectations with a small set of weighted samples --…
The mean-field theory of Kinetically-Constrained-Models is developed by considering the Fredrickson-Andersen model on the Bethe lattice. Using certain properties of the dynamics observed in actual numerical experiments we derive asymptotic…
To explore the limitations of the mean field approximation, frequently used in \textit{ab initio} molecular electronics calculations, we study an out-of-equilibrium Anderson impurity model in a scattering formalism. We find regions in the…
We apply the Bethe-Peierls approximation to the problem of the inverse Ising model and show how the linear response relation leads to a simple method to reconstruct couplings and fields of the Ising model. This reconstruction is exact on…
We study a one--dimensional Ising spin systems with ferromagnetic, long--range interaction decaying as $n^{-2+\a}$, $\a \in [0,\frac 12]$, in the presence of external random fields. We assume that the random fields are given by a collection…
We investigate families of generalized mean--field theories that can be formulated using the Peierls--Bogoliubov inequality. For test--Hamiltonians describing mutually non--interacting subsystems of increasing size, the thermodynamics of…
The statement of the mean field approximation theorem in the mean field theory of Markov processes particularly targets the behaviour of population processes with an unbounded number of agents. However, in most real-world engineering…
The spin glass behavior near zero temperature is a complicated matter. To get an easier access to the spin glass order parameter $Q(x)$ and, at the same time, keep track of $Q_{ab}$, its matrix aspect, and hence of the Hessian controlling…
We investigate the effect of quenched dilution on the critical and spinodal points in the infinite range (mean-field) and long-range (near-mean-field) Ising model. We find that unlike the short-range Ising model, the effect of the dilution…
We derive mean-field equations for a general class of ferromagnetic spin systems with an explicit error bound in finite volumes. The proof is based on a link between the mean-field equation and the free convolution formalism of random…
The 1-arm exponent $\rho$ for the ferromagnetic Ising model on $\mathbb{Z}^d$ is the critical exponent that describes how fast the critical 1-spin expectation at the center of the ball of radius $r$ surrounded by plus spins decays in powers…