Maxwell construction for scalar field theories with spontaneous symmetry breaking
Open accessAbstract
Using a nonperturbative approximation for the partition function of a complex scalar model, which features spontaneous symmetry breaking, we explicitly derive the flattening of the effective potential in the region limited by the minima of the bare potential. This flattening occurs in the limit of infinite volume and is a consequence of the summation over the continuous set of saddle points which dominate the partition function. We also prove the convexity of the effective potential and generalize the Maxwell construction for scalar theories with $O(N)$ symmetry. Finally, we discuss why the flattening of the effective potential cannot occur in the Abelian Higgs theory.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Tunnelling between degenerate vacua is at the origin of convexity of the effective potential and restoration of a symmetric true vacuum.
“while the second is at the origin of convexity of the effective potential [2-11] and therefore restoration of a symmetric true vacuum.”
From Double-well instantons in finite volume (2024) · cites this paper as [9]
The Introduction (p. 2) and Conclusions (p. 19) link summation over degenerate vacua to a convex, flattened effective potential. They describe a superposition of vacua, not tunnelling; Section 3.2 (p. 16) treats a symmetry-restoring vacuum as a possibility under a particular large-N limit, not as a general consequence. The printed citation is attached to convexity, which this source supports, but it does not establish the claim's fuller mechanism and conclusion. (LLM, conf=0.84)
Experimental — accuracy not yet measured
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
No references could be resolved yet.
Research works printed but not linked: 7
- [4][4] V. A. Miransky, Singapore, Singapore: World Scientific (1993) 533 p -
- [5][5] M. T. M. van Kessel, arXiv:0810.1412 [hep-ph]. - · arXiv
- [7][7] J. Alexandre, Phys. Rev. D 86 (2012) 025028 [arXiv:1205.1160 [hep-th]]. - · arXiv
- [9][9] A. Rajantie and D. J. Weir, Phys. Rev. D 82 (2010) 111502 [arXiv:1006.2410 [hep-lat]]. - · arXiv
- [14][14] E. Brezin, J. C. Le Guillou and J. Zinn-Justin, In *Phase Transitions and Critical Phenomena, Vol.6*, Academic Press, London 1976, 125-247. -
- [15][15] J. F. Donoghue, arXiv:1209.3511 [gr-qc]. - · arXiv
- [16][16] C. Wetterich, Nucl. Phys. B 352 (1991) 529; J. Alexandre, V. Branchina and J. Polonyi, Phys. Lett. B 445 (1999) 351 [cond-mat/9803007]; D. F. Litim, J. M. Pawlowski and L. Vergara, hep-th/0602140; V. Pangon, S. Nagy, J. Polonyi and K. Sailer, Int. J. Mod. Phys. A 26 (2011) 1327 [arXiv:0907.0144 [hep-th]]; - · arXiv
Cited by
Sorted by citations
Convexity, gauge-dependence and tunneling rates
Plascencia, A. D., & Tamarit, C. (2016) · Journal of High Energy Physics · doi:10.1007/jhep10(2016)099 · Cited by 64 · see citing works
Symmetry restoration, tunneling, and the null energy condition
Alexandre, J., & Polonyi, J. (2022) · Physical Review D · doi:10.1103/physrevd.106.065008 · Cited by 8 · see citing works
Self-citationDouble-well instantons in finite volume
Ai, W.-Y., Alexandre, J., Carosi, M., Garbrecht, B., & Pla, S. (2024) · Journal of High Energy Physics · doi:10.1007/jhep05(2024)099 · Cited by 6 · see citing works
Self-citation
- Authors
- Alexandre, J., & Tsapalis, A.
- Affiliations
- King's College London (GB)
- Hellenic Naval Academy (GR)
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2013-01-25
- Volume
- 87
- Issue
- 2
- ISSN
- 0556-2821 (ISSN-L)
- 1550-7998
- 1550-2368
- OpenAlex
- W1970403079
- Cited by
- 21
- References
- 0
- Citations by year
- 2025: 2 · 2024: 3 · 2023: 3 · 2022: 2 · 2021: 1 · 2019: 2 · 2018: 1 · 2017: 1 · 2016: 3 · 2015: 3
- FWCI
- 0.91
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Research Portal (King's College London) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Science and Technology Facilities Council (ST/J002798/1)
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Particle physics theoretical and experimental studies
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Quantum Chromodynamics and Particle Interactions
- Keywords
- Maxwell construction, spontaneous symmetry breaking, complex scalar field theory, saddle points, O(N) symmetry, Abelian Higgs model
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
