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Gradient models with non-convex interactions
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Adams, S. (Stefan) (2010) Gradient models with non-convex interactions. In: 16th International Congress on Mathematical Physics, Prague, Czech Republic, August 03-08, 2009. Published in: XVIth International Congress on Mathematical Physics pp. 352-356. ISBN 9789814304627. doi:10.1142/9789814304634_0022
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Official URL: https://doi.org/10.1142/9789814304634_0022
Abstract
We outline recent results in collaboration with R.Kotecky and S. Muller in [1] and [2] about gradient models on an integer lattice with non-convex interactions. These Gibbsian models (continuous Ising models) emerge in various branches of physics and mathematics, with a particular frequency in quantum field theory. Our attention is however mostly devoted to interfaces, of which a massless field is an effective modelisation, however the motivation stems considering vector valued fields as displacements for atoms of crystal structures and the study of the Cauchy-Born rule for these models. For the interface case we prove the strict convexity of the surface tension (free energy) for low enough temperatures and small enough tilts using multi-scale (renormalisation group analysis) techniques. This is the complementary study of the high temperature regime in [3] and it is an extension of Funaki and Spohn's result [4].
Item Type: | Conference Item (Poster) | ||||
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Subjects: | Q Science > QC Physics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | XVIth International Congress on Mathematical Physics | ||||
Publisher: | World Scientific Publishing Co. Pte. Ltd. | ||||
ISBN: | 9789814304627 | ||||
Editor: | Exner, P | ||||
Official Date: | 2010 | ||||
Dates: |
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Number of Pages: | 5 | ||||
Page Range: | pp. 352-356 | ||||
DOI: | 10.1142/9789814304634_0022 | ||||
Status: | Not Peer Reviewed | ||||
Publication Status: | Published | ||||
Conference Paper Type: | Poster | ||||
Title of Event: | 16th International Congress on Mathematical Physics | ||||
Type of Event: | Other | ||||
Location of Event: | Prague, Czech Republic | ||||
Date(s) of Event: | August 03-08, 2009 | ||||
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