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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| 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): |  Creative Commons - CC BY - Namensnennung 4.0 International |
