A geometrical picture for finite-dimensional spin glasses
Laboratoire de Physique Théorique et Modèles Statistiques,
Université Paris-Sud F-91405 Orsay, France
Accepted: 13 January 2000
A controversial issue in spin glass theory is whether mean field correctly describes 3-dimensional spin glasses. If it does, how can replica symmetry breaking arise in terms of spin clusters in Euclidean space? Here we argue that there exist system-size low-energy excitations that are “sponge-like”, generating multiple valleys separated by diverging energy barriers. The droplet model should be valid for length scales smaller than the size of the system (), but nevertheless there can be system-size excitations of constant energy without destroying the spin glass phase. The picture we propose then combines droplet-like behavior at finite length scales with a potentially mean-field behavior at the system-size scale.
PACS: 75.10.Nr – Spin-glass and other random models / 64.70.Pf – Glass transitions
© EDP Sciences, 2000