Inhomogeneous condensation in the Gross-Neveu model in noninteger spatial dimensions 1 ≤ d < 3

  • The Gross-Neveu model in the N→∞ approximation in d=1 spatial dimensions exhibits a chiral inhomogeneous phase (IP), where the chiral condensate has a spatial dependence that spontaneously breaks translational invariance and the Z2 chiral symmetry. This phase is absent in d=2, while in d=3 its existence and extent strongly depends on the regularization and the value of the finite regulator. This work connects these three results smoothly by extending the analysis to non-integer spatial dimensions 1≤d<3, where the model is fully renormalizable. To this end, we adapt the stability analysis, which probes the stability of the homogeneous ground state under inhomogeneous perturbations, to non-integer spatial dimensions. We find that the IP is present for all d<2 and vanishes exactly at d=2. Moreover, we find no instability towards an IP for 2≤d<3, which suggests that the IP in d=3 is solely generated by the presence of a regulator.

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Metadaten
Author:Laurin PannulloORCiDGND
URN:urn:nbn:de:hebis:30:3-794422
URL:https://arxiv.org/abs/2306.16290v2
ArXiv Id:http://arxiv.org/abs/2306.16290v2
Parent Title (English):arXiv
Publisher:arXiv
Document Type:Preprint
Language:English
Date of Publication (online):2023/08/05
Date of first Publication:2023/08/05
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2024/02/22
Issue:2306.16290 Version 2
Edition:Version 2
Page Number:14
HeBIS-PPN:516154540
Institutes:Physik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
Sammlungen:Universitätspublikationen
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International