On the massive sine-Gordon equation in all regions of collapse
type: Item
instance of: scholarly article
title: On the massive sine-Gordon equation in all regions of collapse
zbMATH Open document ID: 0636.35072
DOI: 10.1007/BF01211104
author: B. George
published in: Communications in Mathematical Physics
publication date: 1986-01-01T00:00:00Z
review text: The paper deals with the two dimensional sine-Gordon model which presents interest in quantum field theory as well as in statistical mechanics, where the potential \[ (1)\quad V_ 0[\Lambda]:=\lambda \int_{\Lambda} : \cos \alpha \phi_{\xi} : d\xi \quad \Lambda \subset {\mathbb{R}}^ 2 \] refers to a two dimensional gas of spinless particles with Yukawa interaction in the grand canonical ensemble. In (1) \(\lambda\) is the activity and the inverse temperature of the gas is such that \(\alpha^ 2=\beta e^ 2\), where \(\pm e\) are the charges of the particles. According to previous papers, the gas is stable for \(\beta e^ 2<4\pi\), while at \(\beta e^ 2=8\pi\) one expects full collapse. The ultraviolet stability for all values \(\alpha^ 2\in [4\pi,8\pi[\) is established by means of renormalization group techniques.
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 81T17
Mathematics Subject Classification ID: 81Q05
Mathematics Subject Classification ID: 81V99
zbMATH DE Number: 4036330
zbMATH Keywords: two dimensional sine-Gordon model
zbMATH Keywords: quantum field theory
zbMATH Keywords: statistical mechanics
zbMATH Keywords: potential
zbMATH Keywords: gas of spinless particles
zbMATH Keywords: Yukawa interaction
zbMATH Keywords: stability
zbMATH Keywords: renormalization group
reviewed by: Pasquale Renno
MaRDI profile type: Publication
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: Classical and quantum statistical mechanics in one and two dimensions: two-component Yukawa- and Coulomb systems.
cites work: Q3703500
cites work: Q3768596
description: scientific article; zbMATH DE number 4036330