Title: The cavity approach to parallel dynamics of Ising spins on a graph
Authors: Neri, Izaak ×
Bollé, Désiré #
Issue Date: 6-Aug-2009
Publisher: Institute of Physics Publishing
Series Title: Journal of Statistical Mechanics issue:8
Article number: P08009
Abstract: We use the cavity method to study the parallel dynamics of disordered Ising models on a graph. In particular, we derive a set of recursive equations in single-site probabilities of paths propagating along the edges of the graph. These equations are analogous to the cavity equations for equilibrium models and are exact on a tree.

On graphs with exclusively directed edges we find an exact expression for the stationary distribution. We present the phase diagrams for an Ising model on an asymmetric Bethe lattice and for a neural network with Hebbian interactions on an asymmetric scale-free graph.

For graphs with a nonzero fraction of symmetric edges the equations can be solved for a finite number of time steps. Theoretical predictions are confirmed by simulations.

Using a heuristic method the cavity equations are extended to a set of equations that determine the marginals of the stationary distribution of Ising models on graphs with a nonzero fraction of symmetric edges. The results from this method are discussed and compared with simulations.
ISSN: 1742-5468
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Theoretical Physics Section
× corresponding author
# (joint) last author

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