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

TL;DR

This study uses large-scale simulations to analyze the ground state interface properties of the diluted Sherrington-Kirkpatrick spin glass, revealing space-filling interfaces and universal energy scaling behavior across different bond occupation probabilities.

Contribution

It provides new insights into the universality and independence of certain critical exponents in the diluted SK spin glass model across varying bond probabilities.

Findings

Interface is space-filling with fractal dimension d_s=1 regardless of p.

Stiffness exponent θ is likely independent of p.

Energy finite-size correction exponent ω varies with p but is universal across disorder types.

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.