The absence of finite-temperature PT in low-dimensional
many-body models

doi:10.1088/0953-8984/13/27/201

TOPICAL REVIEW

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

Axel Gelfert et al 2001 J. Phys.: Condens. Matter 13 R505-R524 doi: 10.1088/0953-8984/13/27/201

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Axel Gelfert^1,2 and Wolfgang Nolting¹
¹ Humboldt University of Berlin, Department of Physics, Invalidenstraße 110, 10115 Berlin, Germany
² Department of History and Philosophy of Science, University of Cambridge, Free School Lane, Cambridge CB2 3RH, UK

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.

Print publication: Issue 27 (9 July 2001)
Received 3 May 2001
Published 22 June 2001

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

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