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Spontaneous breakdown of continuous symmetries near two dimensions
Abstract
The long-distance properties of classical Heisenberg ferromagnets below the transition point are related to a continuous-field theory, the nonlinear $\ensuremath{\sigma}$ model. The renormalizability of this model in two dimensions and its ultraviolet asymptotic freedom are used to derive renormalization-group equations valid above $d=2$. It is argued that this model is renormalizable up to four dimensions. The scaling properties which incorporate critical and Goldstone singularities follow. Explicit calculations of exponents and of correlation functions in powers of $d\ensuremath{-}2$ are given. A technique is proposed to make calculations in the symmetric phase applicable even in two dimensions.
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“This is consistent with the fact that the circle reduced theory (keeping only zero KK modes), namely the O(N ) vector model in d = 2 (equivalent to the O(N ) σ-model in the IR) famously has a mass gap for N ≥ 3 [52][53][54][55][56][57][58][59].”
From Casimir energy and modularity in higher-dimensional conformal field theories (2023) · cites this paper as [54]
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Cited by
Non-perturbative renormalization flow in quantum field theory and statistical physics
Berges, J., Tetradis, N., & Wetterich, C. (2002) · Physics Reports · doi:10.1016/s0370-1573(01)00098-9 · Cited by 1,548
The nonperturbative functional renormalization group and its applications
Dupuis, N., Canet, L., Eichhorn, A., Metzner, W., Pawlowski, J. M., Tissier, M., & Wschebor, N. (2021) · Physics Reports · doi:10.1016/j.physrep.2021.01.001 · Cited by 660
Casimir energy and modularity in higher-dimensional conformal field theories
Luo, C., & Wang, Y. (2023) · Journal of High Energy Physics · doi:10.1007/jhep07(2023)028 · Cited by 27
Metadata
- Authors
- Brézin, E., & Zinn-Justin, J.
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 1976-10-01
- Volume
- 14
- Issue
- 7
- Pages
- 3110-3120
- ISSN
- 0556-2805
- Cited by
- 599
- References
- 0
- Language
- en
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- CoChat. (2026). Citation check: Spontaneous breakdown of continuous symmetries near two dimensions. https://app.cochat.ai/papers/10.1103/physrevb.14.3110
- The paper
- Brézin, E., & Zinn-Justin, J. (1976). Spontaneous breakdown of continuous symmetries near two dimensions. Physical Review B. https://doi.org/10.1103/physrevb.14.3110
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
