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

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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.

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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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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Critical indices for Dyson's asymptotically-hierarchical models

Abstract

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