Ground state interface exponents of the diluted Sherrington-Kirkpatrick spin glass

Abstract

We present a large-scale simulation of the ground state interface properties of the diluted Sherrington-Kirkpatrick spin glass of Gaussian disorder for a broad range of the bond occupation probability $p$ using the strong disorder renormalization group and the population annealing Monte Carlo methods. We find that the interface is space-filling independent of $p$, i.e., the fractal dimension $d_s=1$. The stiffness exponent $\theta$ is likely also independent of $p$, despite that the energy finite-size correction exponent $\omega$ varies with $p$ as recently found. The energy finite-size scaling is also analyzed and compared with that of the $\pm J$ disorder, finding that the thermodynamic energy is universal in both $p$ and the disorder, and the exponent $\omega$ varies with $p$ but is universal in the disorder.