The State(s) of Replica Symmetry Breaking: Mean Field Theories vs. Short-Ranged Spin Glasses

Details The State(s) of Replica Symmetry Breaking: Mean Field Theories vs. Short-Ranged Spin Glasses The State(s) of Replica Symmetry Breaking: Mean Field Theories vs. Short-Ranged Spin Glasses

2001-05-14

arxiv.org/abs/cond-mat/0105282v3

Physics

Condensed Matter

Disordered Systems and Neural Networks

32 pages (LaTeX); 3 figures; previously posted under the title ``Replica Symmetry Breaking's New Clothes''; revisions made for

Scientific paper

We prove the impossibility of recent attempts to decouple the Replica Symmetry Breaking (RSB) picture for finite-dimensional spin glasses from the existence of many thermodynamic (i.e., infinite-volume) pure states while preserving another signature RSB feature --- space filling relative domain walls between different finite-volume states. Thus revisions of the notion of pure states cannot shield the RSB picture from the internal contradictions that rule out its physical correctness in finite dimensions at low temperature in large finite volume.

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