Numerical simulations of Ising spin glasses with free boundary conditions: the role of droplet excitations and domain walls

TL;DR

This study uses numerical simulations to analyze the effects of droplet excitations and domain walls on the ordering of short-range Edwards-Anderson spin glasses, highlighting the dominant role of droplet excitations with free boundary conditions.

Contribution

It demonstrates that low-energy droplet excitations primarily influence small overlaps in spin glasses, especially when using free boundary conditions to reduce domain-wall effects.

Findings

Droplet excitations dominate small overlaps in spin glasses.

Free boundary conditions reduce domain-wall contributions.

Finite-size effects are stronger with free boundary conditions.

Abstract

The relative importance of the contributions of droplet excitations and domain walls on the ordering of short-range Edwards-Anderson spin glasses in three and four dimensions is studied. We compare the overlap distributions of periodic and free boundary conditions using population annealing Monte Carlo. For system sizes up to about 1000 spins, spin glasses show non-trivial spin overlap distributions. Periodic boundary conditions can trap diffusive domain walls which can contribute to small spin overlaps, and the other contribution is the existence of low-energy droplet excitations within the system. We use free boundary conditions to minimize domain-wall effects, and show that low-energy droplet excitations are the major contribution to small overlaps in numerical simulations. Free boundary conditions has stronger finite-size effects, and is likely to have the same thermodynamic limit with periodic boundary conditions.