A geometrical picture for finite-dimensional spin glasses

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2000 EDP Sciences
, , Citation J. Houdayer and O. C. Martin 2000 EPL 49 794 DOI 10.1209/epl/i2000-00221-7

0295-5075/49/6/794

Abstract

A controversial issue in spin glass theory is whether mean field correctly describes 3-dimensional spin glasses. If it does, how can replica symmetry breaking arise in terms of spin clusters in Euclidean space? Here we argue that there exist system-size low-energy excitations that are "sponge-like", generating multiple valleys separated by diverging energy barriers. The droplet model should be valid for length scales smaller than the size of the system (θ > 0), but nevertheless there can be system-size excitations of constant energy without destroying the spin glass phase. The picture we propose then combines droplet-like behavior at finite length scales with a potentially mean-field behavior at the system-size scale.

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