Answer to Comment on "Ultrametricity in the Edwards-Anderson Model" arXiv:0709.0894

TL;DR

This paper defends previous evidence of ultrametricity in the 3D Edwards-Anderson model against a comment, clarifying the scaling law approach and demonstrating the absence of replica symmetry breaking in 2D at positive temperature.

Contribution

It clarifies the scaling law method for ultrametricity and extends the analysis to 2D, showing the expected lack of RSB at positive temperature.

Findings

Ultrametric features vanish with increasing volume in 2D.

Scaling law approach confirms no RSB in 2D at positive temperature.

Previous ultrametricity evidence in 3D remains valid.

Abstract

This reply shows that the argument presented in the comment by Jorg and Krzakala (cond mat 0709.0894) cannot be used to weaken the results presented in our paper on ultrametricity evidence in the 3d Edwards Anderson model (PRL 99, 057206, 2007; cond-mat/0607376). Our work in fact was mainly based on identifying the scaling law that governs the large volume approach to ultrametricity while NO asymptotic analysis has been done in (cond mat 0709.0894). We show here that the same method we used in our paper, when properly applied to the 2d case, reveals the expected lack of RSB picture at positive temperature, despite the fact that for a fixed finite volume some ultrametric features might still be seen in the joint overlap probability distribution. Those features disappear for increasing volume or when the system is away from the critical curve in the (T,d) plane.