Mean-Field Criticality Explained by Random Matrices Theory

Random-field Blume-Capel model: Mean-field theory.

Weighted Mean Field Theory for the Random Field Ising Model

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 critical behavior arising from the weighted sum. The resulting exponents are calculated.

Mean-field theory for scale-free random networks

Random networks with complex topology are common in Nature, describing systems as diverse as the world wide web or social and business networks. Recently, it has been demonstrated that most large networks for which topological information is available display scale-free features. Here we study the scaling properties of the recently introduced scale-free model, that can account for the observed ...

Mean Field Theory for Random Recurrent Spiking Neural Networks

Recurrent spiking neural networks can provide biologically inspired model of robot controller. We study here the dynamics of large size randomly connected networks thanks to ”mean field theory”. Mean field theory allows to compute their dynamics under the assumption that the dynamics of individual neuronsare stochastically independent. We restrict ourselves to the simple case of homogeneous cen...

Mean-field theory of random close packings of axisymmetric particles.

Finding the optimal random packing of non-spherical particles is an open problem with great significance in a broad range of scientific and engineering fields. So far, this search has been performed only empirically on a case-by-case basis, in particular, for shapes like dimers, spherocylinders and ellipsoids of revolution. Here we present a mean-field formalism to estimate the packing density ...