Comment on "Ultrametricity in the Edwards-Anderson Model"

TL;DR

This paper critically examines claims of ultrametricity in the 3D Edwards-Anderson spin glass model, showing similar evidence in 2D where no spin glass phase exists, thus questioning the original interpretation.

Contribution

It demonstrates that the relations indicating ultrametricity are not unique to the 3D EA model and can occur in 2D, challenging previous conclusions about the model's structure.

Findings

Relations used as evidence for ultrametricity are also fulfilled in 2D EA model.

The 2D EA model shows no spin glass phase at finite temperature.

Data does not conclusively support ultrametricity in 3D EA model.

Abstract

In a recent interesting Letter Contucci {\it et al.} have investigated several properties of the three-dimensional (3d) Edwards-Anderson (EA) Ising spin glass. They claim to have found strong numerical evidence for the presence of a complex ultrametric structure similar to the one described by the replica symmetry breaking solution of the mean field model. We illustrate by numerical simulations that the relations used by Contucci {\it et al.} as evidence for an ultrametric structure in the 3d EA model are fulfilled to similar accuracy in the two-dimensional EA model, which is well-described by the droplet picture and has no spin glass phase at finite temperature. We conclude that the data presented in the Contucci {\it et al.} Letter is not sufficient to dismiss the possibility that, e.g., the droplet model might describe the behavior of the 3d EA model.