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Critical indices for Dyson's asymptotically-hierarchical models

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Abstract

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.

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Authors and Affiliations

  1. Landau, Theoretical Physics Institute, V334, Moscow, URSS

    P. M. Bleher & Ya. G. Sinai

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  1. P. M. Bleher
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  2. Ya. G. Sinai
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Communicated by G. Gallavotti

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Bleher, P.M., Sinai, Y.G. Critical indices for Dyson's asymptotically-hierarchical models. Commun.Math. Phys. 45, 247–278 (1975). https://doi.org/10.1007/BF01608331

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  • DOI: https://doi.org/10.1007/BF01608331

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