Mathematical Rigor in Physics: Putting Exact Results in Their Place
Gelfert, Axel (2005) Mathematical Rigor in Physics: Putting Exact Results in Their Place. In [2004] Philosophy of Science Assoc. 19th Biennial Meeting - PSA2004: Contributed Papers (Austin, TX; 2004): PSA 2004 Contributed Papers, Austin, Texas.
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Abstract
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.
| 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 |
| Conferences and Volumes: | [2004] Philosophy of Science Assoc. 19th Biennial Meeting - PSA2004: Contributed Papers (Austin, TX; 2004): PSA 2004 Contributed Papers |
| ID Code: | 2160 |
| Deposited By: | Gelfert, Axel |
| Deposited On: | 16 January 2005 |
| Additional Information: | This is the final version as it will appear in Philosophy of Science (Proceedings, PSA 2004). |
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