On Small Perturbations of a Spin Glass System

Details On Small Perturbations of a Spin Glass System On Small Perturbations of a Spin Glass System

2009-02-02

arxiv.org/abs/0902.0294v1

J. Stat. Phys. 135 (2009) 1167-1180

Physics

Mathematical Physics

15 pages

Scientific paper

10.1007/s10955-009-9694-4

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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