Fluctuations induce transitions in frustrated sparse networks

Details Fluctuations induce transitions in frustrated sparse networks Fluctuations induce transitions in frustrated sparse networks

2009-11-26

arxiv.org/abs/0911.5144v1

Fluctuation and noise letter, vol.8 (2008)

Physics

Condensed Matter

Disordered Systems and Neural Networks

Scientific paper

We analyze, by means of statistical mechanics, a sparse network with random competitive interactions among dichotomic variables pasted on the nodes, namely a Viana-Bray model. The model is described by an infinite series of order parameters (the multi-overlaps) and has two tunable degrees of freedom: the noise level and the connectivity (the averaged number of links). We show that there are no multiple transition lines, one for every order parameter, as a naive approach would suggest, but just one corresponding to ergodicity breaking. We explain this scenario within a novel and simple mathematical technique via a driving mechanism such that, as the first order parameter (the two replica overlap) becomes different from zero due to a real second order phase transition (with properly associated diverging rescaled fluctuations), it enforces all the other multi-overlaps toward positive values thanks to the strong correlations which develop among themselves and the two replica overlap at the critical line.

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