Scaling of stiffness energy for 3d +/-J Ising spin glasses

TL;DR

This paper investigates the scaling behavior of ground state stiffness energy in 3D +/-J Ising spin glasses, providing evidence for a finite-temperature phase transition based on extensive computational analysis.

Contribution

It introduces a combined genetic algorithm and Cluster-Exact Approximation method to accurately compute ground states up to size 1000, revealing the stiffness energy scaling exponent.

Findings

Ground state energies are accurately computed for large systems.

The stiffness energy scales as D ~ L^0.19, indicating a phase transition.

Supports the existence of a finite-temperature spin-glass transition in 3D.

Abstract

Large numbers of ground states of 3d EA Ising spin glasses are calculated for sizes up to 10^3 using a combination of a genetic algorithm and Cluster-Exact Approximation. A detailed analysis shows that true ground states are obtained. The ground state stiffness (or domain wall) energy D is calculated. A D ~ L^t behavior with t=0.19(2) is found which strongly indicates that the 3d model has an equilibrium spin-glass-paramagnet transition for non-zero T_c.