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Small Perturbations of a Spin Glass System

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Abstract

We show through a simple example that perturbations of the Hamiltonian of a spin glass which cannot be detected at the level of the free energy can completely alter the behavior of the overlap. In particular, perturbations of order O(log N), with N→∞ the size of the system, suffice to have ultrametricity emerge in the thermodynamical limit.

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Authors and Affiliations

  1. Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., NY, 10012, New York, USA

    Louis-Pierre Arguin

  2. Institute of Applied Mathematics, University of Bonn, Wegelerstr. 6, 53115, Bonn, Germany

    Nicola Kistler

Authors
  1. Louis-Pierre Arguin
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  2. Nicola Kistler
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Corresponding author

Correspondence to Louis-Pierre Arguin.

Additional information

L.-P. Arguin’s research was supported by the NSF grant DMS-0604869.

N. Kistler’s research was supported by the Deutsche Forschungsgemeinschaft, no. DFG GZ BO 962/5-3.

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Arguin, LP., Kistler, N. Small Perturbations of a Spin Glass System. J Stat Phys 135, 1167–1180 (2009). https://doi.org/10.1007/s10955-009-9694-4

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  • DOI: https://doi.org/10.1007/s10955-009-9694-4

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