Ultrametricity Between States at Different Temperatures in Spin-Glasses

Details Ultrametricity Between States at Different Temperatures in Spin-Glasses Ultrametricity Between States at Different Temperatures in Spin-Glasses

2002-07-02

arxiv.org/abs/cond-mat/0207071v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

18 pages, submitted to EPJB

Scientific paper

10.1140/epjb/e2002-00274-x

We prove the existence of correlations between the equilibrium states at different temperatures of the multi-$p$-spin spherical spin-glass models with continuous replica symmetry breaking: there is no chaos in temperature in these models. Furthermore, the overlaps satisfy ultrametric relations. As a consequence the Parisi tree is essentially the same at all temperatures with lower branches developing when lowering the temperature. We conjecture that the reference free energies of the clusters are also fixed at all temperatures as in the generalized random-energy model.

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