Spin Glasses at the Bond Percolation Threshold

Low energy excitations for the Edwards-Anderson model on hyper- cubic lattices at the bond percolation threshold $p_c$ are investigated. At $T=0$, $p_c$ separates paramagnetic and spin glass phases. At the ``edge'' of the ordered state, these excitations are characterized by a distinct scaling exponent. This exponent allows to determine the shape of the phase boundary, $T_c(p)\sim(p-p_{c})^\phi$, for $p\to p_c^+$, which is experimentally measurable in $d=3$. At $p_c$, very large spin glass systems can be studied with an {\it exact} reduction algorithm\footnote{Europhys. Lett. {\bf 67}, 453 (2004)} to produce accurate scaling behavior. For more information, see http://www.physics.emory.edu/faculty/boettcher/