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Universal structures in some mean field spin glasses and an application


Bolthausen, E; Kistler, N (2008). Universal structures in some mean field spin glasses and an application. Journal of Mathematical Physics, 49(12):125205.

Abstract

We discuss a spin glass reminiscent of the random energy model (REM), which allows, in particular, to recast the Parisi minimization into a more classical Gibbs variational principle, thereby shedding some light into the physical meaning of the order parameter of the Parisi theory. As an application, we study the impact of an extensive cavity field on Derrida's REM: Despite its simplicity, this model displays some interesting features such as ultrametricity and chaos in temperature.

Abstract

We discuss a spin glass reminiscent of the random energy model (REM), which allows, in particular, to recast the Parisi minimization into a more classical Gibbs variational principle, thereby shedding some light into the physical meaning of the order parameter of the Parisi theory. As an application, we study the impact of an extensive cavity field on Derrida's REM: Despite its simplicity, this model displays some interesting features such as ultrametricity and chaos in temperature.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:chaos, free energy, random processes, spin glasses, variational techniques
Language:English
Date:2008
Deposited On:09 Nov 2009 00:12
Last Modified:20 May 2016 10:46
Publisher:American Institute of Physics
ISSN:0022-2488
Additional Information:Special Issue: Statistical Mechanics on Random Structures.- Copyright 2008 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Journal of Mathematical Physics, 49(12):125205. and may be found at http://jmp.aip.org/resource/1/jmapaq/v49/i12/p125205_s1?isAuthorized=no
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1063/1.2973818
Related URLs:http://arxiv.org/abs/0806.2446

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