The DOI matches its Crossref record; 155 of the 155 references it cites were found in a registry or an index.
How generic scale invariance influences quantum and classical phase transitions
Open accessAbstract
This review discusses a paradigm that has become of increasing importance in the theory of quantum phase transitions, namely, the coupling of the order-parameter fluctuations to other soft modes and the resulting impossibility of constructing a simple Landau-Ginzburg-Wilson theory in terms of the order parameter only. The soft modes in question are manifestations of generic scale invariance, i.e., the appearance of long-range order in whole regions in the phase diagram. The concept of generic scale invariance and its influence on critical behavior is explained using various examples, both classical and quantum mechanical. The peculiarities of quantum phase transitions are discussed, with emphasis on the fact that they are more susceptible to the effects of generic scale invariance than their classical counterparts. Explicit examples include the quantum ferromagnetic transition in metals, with or without quenched disorder; the metal-superconductor transition at zero temperature; and the quantum antiferromagnetic transition. Analogies with classical phase transitions in liquid crystals and classical fluids are pointed out, and a unifying conceptual framework is developed for all transitions that are influenced by generic scale invariance.
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Cites
Phase Transitions and Critical Phenomena
(2016) · Statistical and Thermal Physics · doi:10.1201/9781439850541-13 · Cited by 11,176
The Physics of Liquid Crystals
de Gennes, P. G., Prost, J., & Pelcovits, R. (1995) · Physics Today · doi:10.1063/1.2808028 · Cited by 9,722
Kubo, R. (1957) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.12.570 · Cited by 9,441
Mermin, N. D., & Wagner, H. (1966) · Physical Review Letters · doi:10.1103/physrevlett.17.1133 · Cited by 8,363
The Physics of Liquid Crystals
Gennes, P. G. D., & Prost, J. (1993) · doi:10.1093/oso/9780198520245.001.0001 · Cited by 8,343
The mathematical theory of non-uniform gases
(1953) · Journal of the Franklin Institute · doi:10.1016/0016-0032(53)90422-0 · Cited by 7,601
Theory of dynamic critical phenomena
Hohenberg, P. C., & Halperin, B. I. (1977) · Reviews of Modern Physics · doi:10.1103/revmodphys.49.435 · Cited by 6,891
Scaling Theory of Localization: Absence of Quantum Diffusion in Two Dimensions
Abrahams, E., Anderson, P. W., Licciardello, D. C., & Ramakrishnan, T. V. (1979) · Physical Review Letters · doi:10.1103/physrevlett.42.673 · Cited by 6,134
Lee, P. A., & Ramakrishnan, T. V. (1985) · Reviews of Modern Physics · doi:10.1103/revmodphys.57.287 · Cited by 6,110
Quantum theory of many-particle systems
Fetter, A. L., & Walecka, J. D. (1971) · Cited by 5,252
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Quantum criticality in heavy-fermion metals
Gegenwart, P., Si, Q., & Steglich, F. (2008) · Nature Physics · doi:10.1038/nphys892 · Cited by 1,309
Hartnoll, S. A., Herzog, C. P., & Horowitz, G. T. (2008) · Journal of High Energy Physics · doi:10.1088/1126-6708/2008/12/015 · Cited by 1,204
Quantum spin dynamics and entanglement generation with hundreds of trapped ions
Bohnet, J. G., Sawyer, B. C., Britton, J. W., Wall, M. L., Rey, A. M., Foss-Feig, M., & Bollinger, J. J. (2016) · Science · doi:10.1126/science.aad9958 · Cited by 546
Rare region effects at classical, quantum and nonequilibrium phase transitions
Vojta, T. (2006) · Journal of Physics A: Mathematical and General · doi:10.1088/0305-4470/39/22/r01 · Cited by 422
Self-citationBrando, M., Belitz, D., Grosche, F. M., & Kirkpatrick, T. R. (2016) · Reviews of Modern Physics · doi:10.1103/revmodphys.88.025006 · Cited by 347
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Metadata
- Authors
- Belitz, D., & Vojta, T.
- Venue
- Reviews of Modern Physics
- Publisher
- American Physical Society (APS)
- Published
- 2005-07
- Volume
- 77
- Issue
- 2
- Pages
- 579-632
- ISSN
- 0034-6861 (ISSN-L)
- 1539-0756
- OpenAlex
- W1851911507
- Cited by
- 283
- References
- 155
- FWCI
- 10.34
- Type
- journal article
- Language
- en
- Open access
- green
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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