A geometrical picture for finite-dimensional spin glasses

E-ISSN： 1286-4854|49|6|794-800

ISSN： 0295-5075

Source： EPL (EUROPHYSICS LETTERS), Vol.49, Iss.6, 2010-03, pp. : 794-800

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Abstract

A controversial issue in spin glass theory is whether mean fieldcorrectly describes 3-dimensional spin glasses.If it does, how can replica symmetry breakingarise in terms of spin clusters inEuclidean space?Here we argue that there exist system-sizelow-energy excitations that are “sponge-like”,generating multiple valleys separated by diverging energybarriers. The droplet model should be valid for length scales smallerthan the size of the system ($\theta > 0$), but neverthelessthere can be system-size excitations of constant energy withoutdestroying the spin glass phase. The picture we propose then combinesdroplet-like behavior at finite length scaleswith a potentially mean-field behavior at the system-size scale.