Renormalization group flow of a hierarchical sine-Gordon model by partial differential equations
type: Item
instance of: scholarly article
title: Renormalization group flow of a hierarchical sine-Gordon model by partial differential equations
zbMATH Open document ID: 0729.35128
DOI: 10.1007/BF02100030
author: T. Kappeler
author: Klaus Pinn
author: Christian Wieczerkowski
published in: Communications in Mathematical Physics
publication date: 1991-01-01T00:00:00Z
review text: We use a renormalization group differential equation to rigorously control the renormalization group flow of a hierarchical lattice Sine- Gordon field theory in the Kosterlitz Thouless phase. As a consequence of an energy estimate, the \(L_ 2\)-norm of the derivative of the effective potential satisfies an exponential upper bound proving that the model is asymptotically free in the infrared limit. More generally, we prove estimates for all derivatives. These estimates provide sufficient information for a detailed analysis of the decay of correlation functions. The method is expected to extend to the full Sine-Gordon model.
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 82C10
Mathematics Subject Classification ID: 81T17
zbMATH DE Number: 4205002
zbMATH Keywords: Sine-Gordon model
MaRDI profile type: Publication
cites work: Renormalization Group and Critical Phenomena. I. Renormalization Group and the Kadanoff Scaling Picture
cites work: The two-dimensional O(N) nonlinear \(\sigma\)-model: Renormalisation and effective actions
cites work: Grad \(\phi\) perturbations of massless Gaussian fields
cites work: Renormalization group in the local potential approximation
cites work: The dipole phase in the two-dimensional hierarchical Coulomb gas: Analyticity and correlations decay
cites work: Q3703500
cites work: Classical and quantum statistical mechanics in one and two dimensions: two-component Yukawa- and Coulomb systems.
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: On the massive sine-Gordon equation in all regions of collapse
cites work: A non-Gaussian renormalization group fixed point for hierarchical scalar lattice field theories
cites work: Q3910965
description: scientific article; zbMATH DE number 4205002