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Against Chaos in Temperature in Mean-Field Spin-Glass Models

Tommaso Rizzo
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Abstract

We study the problem of chaos in temperature in some mean-field spin-glass models by means of a replica computation over a model of coupled systems. We propose a set of solutions of the saddle point equations which are intrinsically non-chaotic and solve a general problem regarding the consistency of their structure. These solutions are relevant in the case of uncoupled systems too, therefore they imply a non-trivial overlap distribution $P(q_{T1T2})$ between systems at different temperatures. The existence of such solutions is checked to fifth order in an expansion near the critical temperature through highly non-trivial cancellations, while it is proved that a dangerous set of such cancellations holds exactly at all orders in the Sherrington-Kirkpatrick (SK) model. The SK model with soft-spin distribution is also considered obtaining analogous results. Previous analytical results are discussed.

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Tommaso Rizzo. 2001-03-19. Against Chaos in Temperature in Mean-Field Spin-Glass Models. https://doi.org/10.1088/0305-4470%2F34%2F27%2F305

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