A geometrical picture for finite-dimensional spin glasses

A controversial issue in spin glass theory is whether mean field correctly describes 3-dimensional spin glasses. Lf 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 dr oplet model should be valid for length scales smaller than the size of the system (theta > 0), but nevertheless there can be system-size excitations o f constant energy without destroying the spin glass phase. The picture we p ropose then combines droplet-like behavior at finite length scales with a p otentially mean-field behavior at the system-size scale.