The absence of finite-temperature phase transitions in low-dimensional many-body models: a survey and new results

2001/06/05 by Axel Gelfert, Wolfgang Nolting · 3 citations
Mathematics · Physics and Astronomy · #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Theoretical and Computational Physics #cond-mat.stat-mech #cond-mat.str-el #math-ph #math.MP

paper · pdf · doi:10.1088/0953-8984/13/27/201

published as J. Phys.: Condens. Matter 13 (2001) R505-R524 · 33 pages; accepted for publication as a Topical Review in Journal of Physics: Condensed Matter

arxiv created 2001/06/05 · openalex publication_date 2001/06/25 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

After a brief discussion of the Bogoliubov inequality and possible generalizations thereof, we present a complete review of results concerning the Mermin-Wagner theorem for various many-body systems, geometries and order parameters. We extend the method to cover magnetic phase transitions in the periodic Anderson model as well as certain superconducting pairing mechanisms for Hubbard films. The relevance of the Mermin-Wagner theorem to approximations in many-body physics is discussed on a conceptual level.

Citations

• Breakdown of the Onsager reaction field theory in two dimensions
• Existence of Long-Range Order in One and Two Dimensions
• Uncertainty principle, quantum fluctuations, and broken symmetries

Cited by

• Absence of Spontaneous Magnetic Order of Lattice Spins Coupled to Itinerant Interacting Electrons in One and Two Dimensions
• Quantum Correlations in Space-Time: Foundations and Applications
• Ferromagnetic Kondo-lattice model