On Small Perturbations of a Spin Glass System

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.

15 pages

References in corpus (4)

• Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model
• An Extended Variational Principle for the SK Spin-Glass Model
• Spin-Glass Stochastic Stability: a Rigorous Proof
• On a nonhierarchical version of the generalized random energy model

Cited by in corpus (2)

• Overlap synchronisation in multipartite random energy models
• Notes on the polynomial identities in random overlap structures