Overlap Equivalence in the Edwards-Anderson Model

Abstract

We study the relative fluctuations of the link overlap and the square standard overlap in the three dimensional Gaussian Edwards-Anderson model with zero external field. We first analyze the correlation coefficient and find that the two quantities are uncorrelated above the critical temperature. Below the critical temperature we find that the link overlap has vanishing fluctuations for fixed values of the square standard overlap and large volumes. Our data show that the conditional variance scales to zero in the thermodynamic limit. This implies that, if one of the two random variables tends to a trivial one (i.e. delta-like distributed), then also the other does and, by consequence, the TNT picture should be dismissed. We identify the functional relation among the two variables using the method of the least squares which turns out to be a monotonically increasing function. Our results show that the two overlaps are completely equivalent in the description of the low temperature phase of the Edwards-Anderson model.

arXiv commentLatex file, 8 Pages, 4 Figures. To appear in: Physical Review Letters

References in corpus (8)

• Nature of the Spin Glass State
• Spin and link overlaps in 3-dimensional spin glasses
• On the Phase Structure of the 3D Edwards Anderson Spin Glass
• On the Effects of a Bulk Perturbation on the Ground State of 3D Ising Spin Glasses
• On the origin of ultrametricity
• Replica equivalence in the Edwards-Anderson model
• Aging in Spin Glasses in three, four and infinite dimensions
• Factorization Properties in the 3D Edwards-Anderson Model

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