Triviality of the Ground State Structure in Ising Spin Glasses

TL;DR

This paper demonstrates that the ground state structure of 3D and 2D Ising spin glasses is trivial, with changes in boundary conditions having negligible effects on distant blocks as system size increases.

Contribution

It provides evidence supporting the droplet theory by showing the triviality of the ground state structure in finite-dimensional Ising spin glasses.

Findings

Probability of ground state change tends to zero with increasing system size

Supports the droplet theory prediction of trivial ground states

Results consistent in both 2D and 3D systems

Abstract

We investigate the ground state structure of the three-dimensional Ising spin glass in zero field by determining how the ground state changes in a fixed finite block far from the boundaries when the boundary conditions are changed. We find that the probability of a change in the block ground state configuration tends to zero as the system size tends to infinity. This indicates a trivial ground state structure, as predicted by the droplet theory. Similar results are also obtained in two dimensions.