The dipole phase in the two-dimensional hierarchical Coulomb gas: Analyticity and correlations decay
type: Item
instance of: scholarly article
title: The dipole phase in the two-dimensional hierarchical Coulomb gas: Analyticity and correlations decay
zbMATH Open document ID: 0646.76091
DOI: 10.1007/BF01454976
author: Giuseppe Benfatto
author: G. Gallavotti
author: Francesco Nicolò
published in: Communications in Mathematical Physics
publication date: 1986-01-01T00:00:00Z
review text: We illustrate the mechanism producing the dipole phase in a two dimensional Coulomb system by a detailed analysis of a hierarchical model. We prove the analyticity of the pressure and of the correlations for \(\alpha^ 2\equiv \beta e^ 2>8\pi\) (i.e. right above the usually conjectured value for the Kosterlitz-Thouless phase transition). We find also a power law decay for the correlations with exponent \(\alpha^ 2/2\pi\) as the hierarchical distance goes to infinity.
Mathematics Subject Classification ID: 76P05
Mathematics Subject Classification ID: 82B40
Mathematics Subject Classification ID: 82B26
zbMATH DE Number: 4055275
zbMATH Keywords: renormalization group theory
zbMATH Keywords: ultraviolet stability
zbMATH Keywords: scalar fields
zbMATH Keywords: dipole phase
zbMATH Keywords: two dimensional Coulomb system
zbMATH Keywords: hierarchical model
zbMATH Keywords: analyticity
zbMATH Keywords: correlations
zbMATH Keywords: Kosterlitz-Thouless phase transition
MaRDI profile type: Publication
cites work: Some probabilistic techniques in field theory
cites work: Ultraviolet stability in Euclidean scalar field theories
cites work: On the massive sine-Gordon equation in the first few regions of collapse
cites work: On the massive sine-Gordon equation in the higher regions of collapse
cites work: Q3703500
cites work: Q3768596
cites work: On the massive sine-Gordon equation in all regions of collapse
full work available at URL: https://doi.org/10.1007/bf01454976
OpenAlex ID: W2022465467
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description: scientific article; zbMATH DE number 4055275