Ground State Structure of Spin Glasses

TL;DR

This paper studies the ground state structure of Ising spin glasses, showing that in large systems the ground state remains stable under boundary condition changes, supporting the droplet theory.

Contribution

It provides numerical evidence that the ground state structure of spin glasses is trivial in large systems, confirming predictions of the droplet theory.

Findings

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

Supports the droplet theory prediction of trivial ground states.

Findings consistent in both two and three dimensions.

Abstract

We investigate the ground state structure of Ising spin glasses in zero magnetic 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, both in two and three dimensions, 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.