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. 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 (θ > 0), 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.