Mean-Field Behaviour in a Local Low-Dimensional Model

Mean Field Behaviour in a Local Low - Dimensional Model Hans - Martin Bröker and Peter Grassberger

We point out a new mechanism which can lead to mean field type behaviour in nonequilibrium critical phenomena. We demonstrate this mechanism on a two-dimensional model which can be understood as a stochas-tic and non-conservative version of the abelian sandpile model of Bak et al. [1]. This model has a second order phase transition whose critical behaviour seems at least partly described by the...

A mean-field model of investor behaviour

In this note we investigate the ability of a mean-field model distilled from the heterogeneous agents model of [7] to simulate stylized facts of financial times series.

Mean Field Analysis of Low Dimensional Systems

For low dimensional systems, (i.e. 2D and, to a certain extent, 1D) it is proved that mean–field theory can provide an asymptotic guideline to the phase structure of actual systems. In particular, for attractive pair interactions that are sufficiently “spead out” according to an exponential (Yukawa) potential it is shown that the energy, free energy and, in particular, the block magnetization (...

Mean-field Behaviour and the Lace Expansion

These lectures describe the lace expansion and its role in proving mean-field critical b ehaviour for selfavoiding walks , lattice trees and animals , and percolation, above their upper cr it ical dimensions. Diagrammatic con dit ions for m ean-field behaviour are also outlined.

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