Inhomogeneous condensation in the Gross-Neveu model in non-integer spatial dimensions 1 ≤ d < 3
- he 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.
Author: | Laurin PannulloORCiDGND |
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URN: | urn:nbn:de:hebis:30:3-794194 |
URL: | https://arxiv.org/abs/2306.16290v1 |
DOI: | https://doi.org/10.48550/arXiv.2306.16290 |
ArXiv Id: | http://arxiv.org/abs/2306.16290v1 |
Parent Title (German): | arXiv |
Publisher: | arXiv |
Document Type: | Preprint |
Language: | English |
Date of Publication (online): | 2023/12/08 |
Date of first Publication: | 2023/12/08 |
Publishing Institution: | Universitätsbibliothek Johann Christian Senckenberg |
Release Date: | 2024/02/22 |
Issue: | 2306.16290 Version 1 |
Edition: | Version 1 |
Page Number: | 14 |
HeBIS-PPN: | 516154532 |
Institutes: | Physik |
Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
Sammlungen: | Universitätspublikationen |
Licence (German): | Creative Commons - CC BY - Namensnennung 4.0 International |