Low Temperature States of Disordered Systems

Abstract

An Edwards-Anderson (EA) spin glass model [EA75] is a disordered Ising model on ℤ ^d whose nearest neighbor couplings $J = \left( {{J_e}:e \in {E^d}} \right)$ are i.i.d. random variables (on some (Ω, ℱ, ν)) with a common symmetric distribution μ (i.e., J _e and — J _e are equidistributed). The most common examples are the Gaussian (where μ is a mean zero normal distribution) and the $\pm \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}}\over J}$ (where $\mu = {1 \over 2}{\delta _{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}}\over J} }} + {1 \over 2}{\delta _{ - \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}}\over J} }}$) models. We place no restrictions on μ beyond symmetry