In this paper we reply to a critical comment by T. Jorg and F. Krzakala to the Letter "Ultrametricity in the Edwards-Anderson Model" PRL 99, 057206 (2007). We show that the procedure developed in the aforementioned paper to detect ultrametricity is able to discriminate the non-ultrametric behavior of the two-dimensional Edwards-Anderson model from the ultrametric three-dimensional one. Moreover, the interesting finding of Jorg and Krzakala that in the two-dimensional Edwards-Anderson model three random configurations have ordered overlaps fulfilling the ultrametric distribution is discussed and an explanation of this phenomenon is proposed.
Answer to Comment on "Ultrametricity in the Edwards-Anderson Model" / P., Contucci; Giardina', Cristian; Giberti, Claudio; G., Parisi; Vernia, Cecilia. - In: PHYSICAL REVIEW LETTERS. - ISSN 0031-9007. - STAMPA. - 100:15(2008), pp. 159702-1-159702-1. [10.1103/PhysRevLett.100.159702]
Answer to Comment on "Ultrametricity in the Edwards-Anderson Model"
GIARDINA', Cristian;GIBERTI, Claudio;VERNIA, Cecilia
2008
Abstract
In this paper we reply to a critical comment by T. Jorg and F. Krzakala to the Letter "Ultrametricity in the Edwards-Anderson Model" PRL 99, 057206 (2007). We show that the procedure developed in the aforementioned paper to detect ultrametricity is able to discriminate the non-ultrametric behavior of the two-dimensional Edwards-Anderson model from the ultrametric three-dimensional one. Moreover, the interesting finding of Jorg and Krzakala that in the two-dimensional Edwards-Anderson model three random configurations have ordered overlaps fulfilling the ultrametric distribution is discussed and an explanation of this phenomenon is proposed.
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