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We discuss the underlying connections among the thermodynamic properties of short-ranged spin glasses, their behavior in large finite volumes, and the interfaces that separate different pure states, and also ground states and low-lying excitations.
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 and 4. We show that such e
We use a non-equilibrium simulation method to study the spin glass transition in three-dimensional Ising spin glasses. The transition point is repeatedly approached at finite velocity $v$ (temperature change versus time) in Monte Carlo simulations st
We present a detailed proof of a previously announced result (C.M. Newman and D.L. Stein, Phys. Rev. Lett. v. 84, pp. 3966--3969 (2000)) supporting the absence of multiple (incongruent) ground state pairs for 2D Edwards-Anderson spin glasses (with ze
We investigate the performance of the recently proposed stationary Fokker-Planck sampling method considering a combinatorial optimization problem from statistical physics. The algorithmic procedure relies upon the numerical solution of a linear secon
We present a mean field model for spin glasses with a natural notion of distance built in, namely, the Edwards-Anderson model on the diluted D-dimensional unit hypercube in the limit of large D. We show that finite D effects are strongly dependent on