Related papers: A statistical theory of the mean field
We develop a statistical theory of the mean field. It is based on the proposition that the mean field can be obtained as an energy average. Moreover, it is assumed that the matrix elements of the residual interaction are random with the…
A recently proposed statistical theory of the mean fields associated with the ground and excited collective states of a generic many-body system is extended by increasing the dimensions of the P-space. In applying the new framework to…
Mean field theory is a device to analyze the collective behavior of a dynamical system comprising many interacting particles. The theory allows to reduce the behavior of the system to the properties of a handful of parameters. In neural…
Simple elastic models of spin-crossover compounds are known empirically to exhibit classical critical behavior. We demonstrate how the long-ranged interactions responsible for this behavior arise naturally upon integrating out mechanical…
A dynamical model of an ecological community is analyzed within a "mean-field approximation" in which one of the species interacts with the combination of all of the other species in the community. Within this approximation the model may be…
We study the random-field Ising model with long-range interactions and show the exactness of the mean-field theory under certain mild conditions. This is a generalization of the result of Mori for the non-random and spin-glass cases. To…
A new mean field statistical mechanics model of two interacting groups of spins is introduced and the phase transition studied in terms of their relative size. A jump of the average magnetization is found for large values of the mutual…
We review some possible improvements of mean field theory for application to nuclear binding systematics. Up to now, microscopic theory has been less successful than models starting from the liquid drop in describing accurately the global…
Microscopic theories beyond mean-field are developed to include pairing, in-medium nucleon-nucleon collisions as well as effects of initial fluctuations of one-body observables on nuclear dynamics. These theories are applied to nuclear…
We study the dynamics of a spin-flip model with a mean field interaction. The system is non reversible, spacially inhomogeneous, and it is designed to model social interactions. We obtain the limiting behavior of the empirical averages in…
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…
The aim of this work is to implement a statistical mechanics theory of social interaction, generalizing econometric discrete choice models. A class of simple mean field discrete models is introduced and discussed both from the theoretical…
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…
The physical properties of granular materials have been extensively studied in recent years. So far, however, there exists no theoretical framework which can explain the observations in a unified manner beyond the phenomenological jamming…
We analyzed the results for finite nuclei and infinite nuclear and neutron matter using the standard $\sigma-\omega$ model and with the effective field theory. For the first time, we have shown here quantitatively that the inclusion of…
All current formulations of nonequilibrium thermodynamics of open chemical reaction networks rely on the assumption of non-interacting species. We develop a general theory which accounts for interactions between chemical species within a…
We consider the mean field theory of the Random Field Ising Model obtained by weighing the many solutions of the mean field equations with Boltzmann-like factors. These solutions are found numerically in three dimensions and we observe…
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…
Analytic treatment of a non-equilibrium random system with large degrees of freedoms is one of most important problems of physics. However, little research has been done on this problem as far as we know. In this paper, we propose a new…
In this Review article, a brief description of the stochastic mean-field theory (SMF) for describing reaction dynamics in low-energy heavy-ion collisions at bombarding energies in the vicinity of the Coulomb barrier is presented. In these…