We present a general theorem restricting properties of interfaces between thermodynamic states and apply it to the spin glass excitations observed numerically by Krzakala-Martin and Palassini-Young in spatial dimensions d=3,4. We show that such excitations, with interface dimension strictly...

We consider zero-temperature, stochastic Ising models σt with nearest-neighbor interactions and an initial spin configuration σ0 chosen from a symmetric Bernoulli distribution (corresponding physically to a deep quench). Whether σ∞ exists, i.e., whether each spin flips only finitely many...

We study the nature and mechanisms of broken ergodicity (BE) in specific random walk models corresponding to diffusion on random potential surfaces, in both one and high dimension. Using both rigorous results and nonrigorous methods, we confirm several aspects of the standard BE picture and show...