Communications in Mathematical Physics

, Volume 45, Issue 3, pp 247–278 | Cite as

Critical indices for Dyson's asymptotically-hierarchical models

  • P. M. Bleher
  • Ya. G. Sinai


It is known that the investigation of the critical point for models of the type of Dyson's hierarchical models is reduced to the solution of some non-linear integral equation. In our previous publication the Gaussian solution was investigated. Here we construct non-Gaussian solutions of the equation and find the expressions for critical indices connected with them. Our procedure permits us to construct meaningful ε-expansions.


Neural Network Statistical Physic Integral Equation Complex System Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • P. M. Bleher
    • 1
  • Ya. G. Sinai
    • 1
  1. 1.Landau, Theoretical Physics InstituteMoscowURSS

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