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

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

2001-06-05

arxiv.org/abs/cond-mat/0106090v1

J. Phys.: Condens. Matter 13 (2001) R505-R524

Physics

Condensed Matter

Strongly Correlated Electrons

33 pages; accepted for publication as a Topical Review in Journal of Physics: Condensed Matter

Scientific paper

10.1088/0953-8984/13/27/201

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.

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