Droplet Phenomenology and Mean Field in a Frustrated and Disordered System

TL;DR

This paper investigates the low-energy excitations in a 3D disordered system, revealing a coexistence of droplet-like behavior at small scales and mean field characteristics at larger scales, through numerical analysis.

Contribution

It provides numerical evidence for the coexistence of droplet phenomenology and mean field behavior in a frustrated disordered system.

Findings

Excitations' energies grow with size, confirming the droplet picture.

Existence of infinite size excitations creating multiple valleys.

Mean field predictions are consistent with certain low-energy states.

Abstract

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.