Droplet Phenomenology and Mean Field in a Frustrated and Disordered System

Physics – Condensed Matter – Disordered Systems and Neural Networks

Scientific paper

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4 pages, 2 figures, to appear in Phys. Rev. Lett

Scientific paper

10.1103/PhysRevLett.81.2554

The low lying excited states of the three-dimensional minimum matching problem are studied numerically. The excitations' energies grow with their size and confirm the droplet picture. However, some low energy, infinite size excitations create multiple valleys in the energy landscape. These states violate the droplet scaling ansatz, and are consistent with mean field predictions. A similar picture may apply to spin glasses whereby the droplet picture describes the physics at small length scales, while mean field describes that at large length scales.

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