Reply to "Comment on Evidence for the droplet picture of spin glasses"

TL;DR

This paper refutes claims that Monte Carlo simulations and Migdal-Kadanoff approximation indicate replica symmetry breaking in 3D Ising spin glasses, demonstrating consistency with the droplet picture instead.

Contribution

It clarifies that both simulation and approximation results align with the droplet model, countering previous claims of replica symmetry breaking evidence.

Findings

MCS results can be explained by the droplet picture.

MKA results are consistent with the droplet model.

Claims of RSB based on these methods are incorrect.

Abstract

Using Monte Carlo simulations (MCS) and the Migdal-Kadanoff approximation (MKA), Marinari et al. study in their comment on our paper the link overlap between two replicas of a three-dimensional Ising spin glass in the presence of a coupling between the replicas. They claim that the results of the MCS indicate replica symmetry breaking (RSB), while those of the MKA are trivial, and that moderate size lattices display the true low temperature behavior. Here we show that these claims are incorrect, and that the results of MCS and MKA both can be explained within the droplet picture.