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Title: UV fixed-point structure of the three-dimensional Thirring model

Abstract

We investigate the UV fixed-point structure of the three-dimensional Thirring model by means of the functional renormalization group. We classify all possible 4-fermi interactions compatible with the present chiral and discrete symmetries and calculate the purely fermionic renormalization group flow using a full basis of fermionic four-point functions in the pointlike limit. Our results show that the UV complete (asymptotically safe) Thirring model lies in a two-dimensional coupling plane which reduces to the conventional Thirring coupling only in the strict large-N{sub f} limit. In addition to the Thirring universality class, which is characterized by one relevant direction (also at finite N{sub f}), two further interacting fixed points occur which may define new universality classes of second-order phase transitions also involving parity-broken phases. The N{sub f} dependence of the Thirring fixed point sheds further light on the existence of an N{sub f}-controlled quantum phase transition above which chiral symmetry remains unbroken for arbitrary large coupling, even though a definite answer will require a direct computation of competing orders.

Authors:
;  [1]
  1. Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universitaet Jena, Max-Wien-Platz 1, 07743 Jena (Germany)
Publication Date:
OSTI Identifier:
21432421
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 82; Journal Issue: 8; Other Information: DOI: 10.1103/PhysRevD.82.085018; (c) 2010 American Institute of Physics; Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CHIRAL SYMMETRY; CHIRALITY; COUPLING; FERMI INTERACTIONS; FERMIONS; MANY-BODY PROBLEM; PARITY; PHASE TRANSFORMATIONS; RENORMALIZATION; SYMMETRY BREAKING; THIRRING MODEL; THREE-DIMENSIONAL CALCULATIONS; BASIC INTERACTIONS; INTERACTIONS; PARTICLE PROPERTIES; SYMMETRY; WEAK INTERACTIONS

Citation Formats

Gies, Holger, and Janssen, Lukas. UV fixed-point structure of the three-dimensional Thirring model. United States: N. p., 2010. Web. doi:10.1103/PHYSREVD.82.085018.
Gies, Holger, & Janssen, Lukas. UV fixed-point structure of the three-dimensional Thirring model. United States. doi:10.1103/PHYSREVD.82.085018.
Gies, Holger, and Janssen, Lukas. Fri . "UV fixed-point structure of the three-dimensional Thirring model". United States. doi:10.1103/PHYSREVD.82.085018.
@article{osti_21432421,
title = {UV fixed-point structure of the three-dimensional Thirring model},
author = {Gies, Holger and Janssen, Lukas},
abstractNote = {We investigate the UV fixed-point structure of the three-dimensional Thirring model by means of the functional renormalization group. We classify all possible 4-fermi interactions compatible with the present chiral and discrete symmetries and calculate the purely fermionic renormalization group flow using a full basis of fermionic four-point functions in the pointlike limit. Our results show that the UV complete (asymptotically safe) Thirring model lies in a two-dimensional coupling plane which reduces to the conventional Thirring coupling only in the strict large-N{sub f} limit. In addition to the Thirring universality class, which is characterized by one relevant direction (also at finite N{sub f}), two further interacting fixed points occur which may define new universality classes of second-order phase transitions also involving parity-broken phases. The N{sub f} dependence of the Thirring fixed point sheds further light on the existence of an N{sub f}-controlled quantum phase transition above which chiral symmetry remains unbroken for arbitrary large coupling, even though a definite answer will require a direct computation of competing orders.},
doi = {10.1103/PHYSREVD.82.085018},
journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 8,
volume = 82,
place = {United States},
year = {2010},
month = {10}
}