Critical indices for Dyson's asymptotically-hierarchical models

P. M. Bleher; Ya G. Sinai

doi:10.1007/BF01608331

Critical indices for Dyson's asymptotically-hierarchical models

P. M. Bleher
, Ya G. Sinai

Research output: Contribution to journal › Article › peer-review

89 Scopus citations

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.

Original language	English (US)
Pages (from-to)	247-278
Number of pages	32
Journal	Communications In Mathematical Physics
Volume	45
Issue number	3
DOIs	https://doi.org/10.1007/BF01608331
State	Published - Oct 1975

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF01608331

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title = "Critical indices for Dyson's asymptotically-hierarchical models",

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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AB - 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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DO - 10.1007/BF01608331

M3 - Article

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EP - 278

JO - Communications In Mathematical Physics

JF - Communications In Mathematical Physics

IS - 3

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Critical indices for Dyson's asymptotically-hierarchical models

Abstract

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