Propagating beliefs in spin glass models

Details Propagating beliefs in spin glass models Propagating beliefs in spin glass models

2002-11-22

arxiv.org/abs/cond-mat/0211500v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

Scientific paper

10.1143/JPSJ.72.1645

We investigate dynamics of an inference algorithm termed the belief propagation (BP) when employed in spin glass (SG) models and show that its macroscopic behaviors can be traced by recursive updates of certain auxiliary field distributions whose stationary state reproduces the replica symmetric solution offered by the equilibrium analysis. We further provide a compact expression for the instability condition of the BP's fixed point which turns out to be identical to that of instability for breaking the replica symmetry in equilibrium when the number of couplings per spin is infinite. This correspondence is extended to a SG model of finite connectivity to determine the phase diagram, which is numerically supported.

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