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

P. M. Bleher; Ja G. Sinai

doi:10.1007/BF01645604

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

P. M. Bleher, Ja G. Sinai

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Abstract

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.

Original language	English (US)
Pages (from-to)	23-42
Number of pages	20
Journal	Communications In Mathematical Physics
Volume	33
Issue number	1
DOIs	https://doi.org/10.1007/BF01645604
State	Published - Mar 1973

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF01645604

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abstract = "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.",

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

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