Communications in Mathematical Physics

, Volume 33, Issue 1, pp 23–42 | Cite as

Investigation of the critical point in models of the type of Dyson's hierarchical models

  • P. M. Bleher
  • Ja. G. Sinai


We consider the classical spin models where the Hamiltonians are small modifications of the Hamiltonians of Dyson's hierarchical models. Under some assumptions we investigate rigorously the neighbourhood of the critical point and find the critical indices. It follows that in the cases under consideration phenomenological Landau's theory of phase transitions is valid.


Neural Network Phase Transition Statistical Physic Complex System Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • P. M. Bleher
    • 1
  • Ja. G. Sinai
    • 1
  1. 1.Landau Institute for Theoretical PhysicsAcademy of SciencesMoscowUSSR

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