Comment on "Ultrametricity in the Edwards-Anderson Model"

Details Comment on "Ultrametricity in the Edwards-Anderson Model" Comment on "Ultrametricity in the Edwards-Anderson Model"

2007-09-06

arxiv.org/abs/0709.0894v1

Phys. Rev. Lett. 100, 159701 (2008)

Physics

Condensed Matter

Disordered Systems and Neural Networks

1 page, 1 figure

Scientific paper

10.1103/PhysRevLett.100.159701

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.

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