As a follow-up of previous work of the authors, we analyse the statistical mechanics model of random spanning forests on random planar graphs. Special emphasis is given to the analysis of the critical behaviour. Exploiting an exact relation with a model of O(-2)-loops and dimers, previously solved by Kostov and Staudacher, we identify critical and multicritical loci, and find them consistent with recent results of Bousquet- Melou and Courtiel. This is also consistent with the KPZ relation, and the Berker-Kadanoff phase in the anti-ferromagnetic regime of the Potts Model on periodic lattices, predicted by Saleur. To our knowledge, this is the first known example of KPZ appearing explicitly to work within a Berker Kadanoff phase. We set up equations for the generating function, at the value t = -1 of the fugacity, which is of combinatorial interest, and we investigate the resulting numerical series, a favourite problem of Tony Guttmann's.

Critical behaviour of spanning forests on random planar graphs / R. Bondesan, S. Caracciolo, A. Sportiello. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - 50:7(2017), pp. 074003.1-074003.51. [10.1088/1751-8121/aa546f]

Critical behaviour of spanning forests on random planar graphs

S. Caracciolo;A. Sportiello
2017

Abstract

As a follow-up of previous work of the authors, we analyse the statistical mechanics model of random spanning forests on random planar graphs. Special emphasis is given to the analysis of the critical behaviour. Exploiting an exact relation with a model of O(-2)-loops and dimers, previously solved by Kostov and Staudacher, we identify critical and multicritical loci, and find them consistent with recent results of Bousquet- Melou and Courtiel. This is also consistent with the KPZ relation, and the Berker-Kadanoff phase in the anti-ferromagnetic regime of the Potts Model on periodic lattices, predicted by Saleur. To our knowledge, this is the first known example of KPZ appearing explicitly to work within a Berker Kadanoff phase. We set up equations for the generating function, at the value t = -1 of the fugacity, which is of combinatorial interest, and we investigate the resulting numerical series, a favourite problem of Tony Guttmann's.
Berker-Kadanoff phase; KPZ; Potts model; random planar graphs; spanning forests; Physics - Statistical Mechanics; Physics - Statistical Mechanics; High Energy Physics - Theory; Mathematical Physics; Mathematics - Combinatorics; Mathematics - Mathematical Physics; Statistical and Nonlinear Physics; Statistics and Probability; Modeling and Simulation; Mathematical Physics; Physics and Astronomy (all)
Settore FIS/02 - Fisica Teorica, Modelli e Metodi Matematici
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/511993
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