Stiffness of the Edwards-Anderson Model in all Dimensions

Stefan Boettcher (Emory University)

Stiffness of the Edwards-Anderson Model in all Dimensions

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arxiv cond-mat/0508061 v2 pith:Y5MCL6I7 submitted 2005-08-01 cond-mat.stat-mech cond-mat.dis-nn

Stiffness of the Edwards-Anderson Model in all Dimensions

Stefan Boettcher (Emory University) This is my paper

classification cond-mat.stat-mech cond-mat.dis-nn

keywords dimensionsglassmodelspinandersoncombinationcompletecomprehensive

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A comprehensive description in all dimensions is provided for the scaling exponent $y$ of low-energy excitations in the Ising spin glass introduced by Edwards and Anderson. A combination of extensive numerical as well as theoretical results suggest that its lower critical dimension is {\it exactly} $d_l=5/2$. Such a result would be an essential feature of any complete model of low-temperature spin glass order and imposes a constraint that may help to distinguish between theories.

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Low energy excitations in a long prism geometry: testing the lower critical dimension of the Ising spin glass
cond-mat.dis-nn 2026-01 conditional novelty 7.0

A long-prism simulation of the 3D Ising spin glass yields lower critical dimension D_lc = 2.49(3), favoring mean-field 5/2 over the droplet-model value ≈2.61.