Aspect-Ratio Scaling and The Stiffness Exponent $\theta$ for Ising Spin Glasses

Abstract

We introduce the technique of aspect-ratio scaling to study the scale-dependence of interfacial energies in Ising spin glasses, and we show how one can use it to determine the stiffness exponent $\theta$ in a clean way, with results that are independent of the domain-wall-forcing boundary conditions imposed on the system. In space dimension d=2 we obtain $\theta = -0.282(3)$ for a Gaussian distribution of exchange interactions.