Grundstate Properties of the 3D Ising Spin Glass

TL;DR

This paper investigates the ground state properties of the 3D Edwards--Anderson Ising spin glass using large-scale simulations, analyzing finite size effects and comparing different theoretical descriptions.

Contribution

It provides new numerical data on ground states of 3D spin glasses and compares finite size scaling with mean field theories.

Findings

Finite size scaling exponent y = 0.74 ± 0.12

Data well described by finite size scaling

Alternative Parisi mean field description remains plausible

Abstract

We study zero--temperature properties of the 3d Edwards--Anderson Ising spin glass on finite lattices up to size $12^3$. Using multicanonical sampling we generate large numbers of groundstate configurations in thermal equilibrium. Finite size scaling with a zero--temperature scaling exponent $y = 0.74 \pm 0.12$ describes the data well. Alternatively, a descriptions in terms of Parisi mean field behaviour is still possible. The two scenarios give significantly different predictions on lattices of size $\ge 12^3$.