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

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arxiv cond-mat/0105282 v3 submitted 2001-05-14 cond-mat.dis-nn cond-mat.stat-mech

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

C.M. Newman (Courant Institute of Mathematical Sciences , New York University , USA) , D.L. Stein (Departments of Physics , Mathematics , University of Arizona This is my paper
classification cond-mat.dis-nn cond-mat.stat-mech
keywords statesbreakingfiniteglassespicturepurereplicaspin
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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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