Domain-wall free energy $\delta F$, entropy $\delta S$, and the correlation function $C_{\mathrm{temp}}$ of $\delta F$ are measured independently in the four-dimensional $\pm J$ Edwards-Anderson (EA) Ising spin glass. The stiffness exponent $\theta$, the fractal dimension of domain walls $d_s$, and the chaos exponent $\zeta$ are extracted from the finite-size scaling analysis of $\delta F$, $\delta S$, and $C_{\mathrm{temp}}$, respectively, well inside the spin-glass phase. The three exponents are confirmed to satisfy the scaling relation $\zeta =d_s/2-\theta$ derived by the droplet theory within our numerical accuracy. We also study bond chaos induced by random variation of bonds, and find that the bond and temperature perturbations yield the universal chaos effects described by a common scaling function and the chaos exponent. These results strongly support the appropriateness of the droplet theory for the description of chaos effect in the EA Ising spin glasses.

• Received 5 November 2004

DOI:https://doi.org/10.1103/PhysRevLett.95.267203