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Mathematical Rigor in Physics: Putting Exact Results in Their Place

Gelfert, Axel (2005) Mathematical Rigor in Physics: Putting Exact Results in Their Place. In: UNSPECIFIED. (In Press)

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The present paper examines the role of exact results in the theory of many-body physics, and specifically the example of the Mermin-Wagner theorem, a rigorous result concerning the absence of phase transitions in low-dimensional systems. While the theorem has been shown to hold for a wide range of many-body models, it is frequently ‘violated’ by results derived from the same models using numerical techniques. This raises the question of how scientists regulate their theoretical commitments in such cases, given that the models, too, are often described as approximations to the underlying ‘full’ many-body problem.

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Item Type: Conference or Workshop Item (UNSPECIFIED)
Gelfert, Axel
Additional Information: This is the final version as it will appear in Philosophy of Science (Proceedings, PSA 2004).
Keywords: rigorous results, mathematical rigor, condensed matter physics, phase transitions, many-body physics, statistical physics, models
Subjects: General Issues > Models and Idealization
Specific Sciences > Physics
Depositing User: Axel Gelfert
Date Deposited: 16 Jan 2005
Last Modified: 07 Oct 2010 15:13
Item ID: 2160
Public Domain: No
Conference Date: 18-20 November 2004
Conference Location: Austin, Texas

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