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A motivic approach to phase transitions in Potts models

Aluffi, Paolo and Marcolli, Matilde (2013) A motivic approach to phase transitions in Potts models. Journal of Geometry and Physics, 63 . pp. 6-31. ISSN 0393-0440. doi:10.1016/j.geomphys.2012.09.003.

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We describe an approach to the study of phase transitions in Potts models based on an estimate of the complexity of the locus of real zeros of the partition function, computed in terms of the classes in the Grothendieck ring of the affine algebraic varieties defined by the vanishing of the multivariate Tutte polynomial. We give completely explicit calculations for the examples of the chains of linked polygons and of the graphs obtained by replacing the polygons with their dual graphs. These are based on a deletion–contraction formula for the Grothendieck classes and on generating functions for splitting and doubling edges.

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Additional Information:© 2012 Elsevier B.V. Received 22 April 2012. Accepted 6 September 2012. Available online 17 September 2012.
Subject Keywords:Potts models; Feynman motives; Grothendieck group; Phase transitions
Record Number:CaltechAUTHORS:20130117-104305431
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Official Citation:Paolo Aluffi, Matilde Marcolli, A motivic approach to phase transitions in Potts models, Journal of Geometry and Physics, Volume 63, January 2013, Pages 6-31, ISSN 0393-0440, 10.1016/j.geomphys.2012.09.003. (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:36450
Deposited By: Ruth Sustaita
Deposited On:17 Jan 2013 19:08
Last Modified:09 Nov 2021 23:22

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