On the Lower Critical Dimension of the Edwards-Anderson Spin Glass

The Edwards-Anderson model of Spin Glasses is studied on dilute hyper-cubic lattices in dimensions $d=2,3,\ldots,7$. Accurate predictions for the stiffness exponent $y_d$ are obtained that describes low-energy excitations. Continuing $y_d$ off the integers shows that its zero is located at $d=5/2$ to within 0.1\%, a prediction that is corroborated by other numerical and theoretical work. \\ Related Publication: Phys. Rev. Lett. {\bf 95}, 197205 (2005). \\ Related Webpage: http://www.physics.emory.edu/faculty/boettcher/ .