Number of thermodynamic states in the three-dimensional Edwards-Anderson spin glass

TL;DR

This study investigates the number of thermodynamic states in the low-temperature phase of the 3D Edwards-Anderson spin glass using Monte Carlo simulations, finding results compatible with both single and multiple state scenarios due to finite-size effects.

Contribution

It provides new simulation data analyzing overlaps with different boundary conditions, offering insights into the debated number of thermodynamic states in the model.

Findings

Results compatible with a single pair of pure states.

Results also compatible with many thermodynamic states.

Finite-size effects are significant in current simulations.

Abstract

The question of the number of thermodynamic states present in the low-temperature phase of the three-dimensional Edwards-Anderson Ising spin glass is addressed by studying spin and link overlap distributions using population annealing Monte Carlo simulations. We consider overlaps between systems with the same boundary condition-which are the usual quantities measured-and also overlaps between systems with different boundary conditions, both for the full systems and also within a smaller window within the system. Our results appear to be fully compatible with a single pair of pure states such as in the droplet/scaling picture. However, our results for whether or not domain walls induced by changing boundary conditions are space filling or not are also compatible with scenarios having many thermodynamic states, such as the chaotic pairs picture and the replica symmetry breaking picture. The differing results for spin overlaps in same and different boundary conditions suggest that finite-size effects are very large for the system sizes currently accessible in low-temperature simulations.