Correspondence between long-range and short-range spin glasses

Short-Range Spin Glasses: Results and Speculations

This paper is divided into two parts. The first part concerns several standard scenarios for how short-range spin glasses might behave at low temperature. Earlier theorems of the authors are reviewed, and some new results presented, including a proof that, in a thermodynamic system exhibiting infinitely many pure states and with the property (such as in replica-symmetrybreaking scenarios) that ...

Short-Range Spin Glasses: The Metastate Approach

We discuss the metastate, a probability measure on thermodynamic states, and its usefulness in addressing difficult questions pertaining to the statistical mechanics of systems with quenched disorder, in particular short-range spin glasses. The possible low-temperature structures of realistic (i.e., short-range) spin glass models are described, and a number of fundamental open questions are pre...

Thermodynamic Identities and Symmetry Breaking in Short-Range Spin Glasses.

We present a technique to generate relations connecting pure state weights, overlaps, and correlation functions in short-range spin glasses. These are obtained directly from the unperturbed Hamiltonian and hold for general coupling distributions. All are satisfied in phases with simple thermodynamic structure, such as the droplet-scaling and chaotic pairs pictures. If instead nontrivial mixed-s...

Thermodynamic Chaos and the Structure of Short-range Spin Glasses

Metastable States in High Order Short-Range Spin Glasses

Abstract. The mean number 〈N〉 of metastable states in higher order shortrange spin glasses is estimated analytically using a variational method introduced by Tanaka and Edwards for very large coordination numbers. For lattices with small connectivities, numerical simulations do not show any significant dependence on the relative positions of the interacting spins on the lattice, indicating thus...