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Journal of Statistical Physics

, Volume 36, Issue 5–6, pp 787–793 | Cite as

Hierarchical models and chaotic spin glasses

  • A. Nihat Berker
  • Susan R. McKay
Articles

Abstract

Renormalization-group studies in position space have led to the discovery of hierarchical models which are exactly solvable, exhibiting nonclassical critical behavior at finite temperature. Position-space renormalization-group approximations that had been widely and successfully used are in fact alternatively applicable as exact solutions of hierarchical models, this realizability guaranteeing important physical requirements. For example, a hierarchized version of the Sierpiriski gasket is presented, corresponding to a renormalization-group approximation which has quantitatively yielded the multicritical phase diagrams of submonolayers on graphite. Hierarchical models are now being studied directly as a testing ground for new concepts. For example, with the introduction of frustration, chaotic renormalization-group trajectories were obtained for the first time. Thus, strong and weak correlations are randomly intermingled at successive length scales, and a new microscopic picture and mechanism for a spin glass emerges. An upper critical dimension occurs via a boundary crisis mechanism in cluster-hierarchical variants developed to have well-behaved susceptibilities.

Key words

Hierarchical models renormalization group Sierpiński gasket frustration chaos spin glass boundary crisis 

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Copyright information

© Plenum Publishing Corporation 1984

Authors and Affiliations

  • A. Nihat Berker
    • 1
  • Susan R. McKay
    • 1
  1. 1.Department of PhysicsMassachusetts Institute of TechnologyCambridge

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