Journal article

Conformal partition functions of critical percolation from D-3 thermodynamic Bethe Ansatz equations

Alexi Morin-Duchesne, Andreas Kluemper, Paul A Pearce

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT | IOP PUBLISHING LTD | Published : 2017

Abstract

Using the planar Temperley-Lieb algebra, critical bond percolation on the square lattice can be reformulated as a loop model. In this form, it is incorporated as Ⅎℳ(2, 3) in the Yang-Baxter integrable family of logarithmic minimal models Ⅎℳ( p, p'). We consider this model of percolation in the presence of boundaries and with periodic boundary conditions. Inspired by Kuniba, Sakai and Suzuki, we rewrite the recently obtained infinite Y-system of functional equations. In this way, we obtain nonlinear integral equations in the form of a closed finite set of TBA equations described by a D3 Dynkin diagram. Following the methods of Klmper and Pearce, we solve the TBA equations for the conformal fi..

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University of Melbourne Researchers

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Awarded by network DYGEST (Dynamics, Geometry and Statistical Physics)


Funding Acknowledgements

AMD was supported by the Belgian Interuniversity Attraction Poles Program P7/18 through the network DYGEST (Dynamics, Geometry and Statistical Physics) and by the FNRS fellowship CR28075116. AMD and AK acknowledge the support of the ERC grant Loop models, integrability and combinatorics and are grateful for the kind hospitality of Paul Zinn-Justin and the LPTHE where early stages of this work were done. AMD and PAP acknowledge the hospitality of the University of Wuppertal and are grateful for the kind hospitality of Holger Frahm at the ITP in Hannover where later stages of this work were done. All authors were supported by DFG through the program FOG 2316. PAP thanks the APCTP, Pohang for hospitality during the writing of this paper. The authors thank Paul Zinn-Justin, Jorgen Rasmussen and Yacine Ikhlef for useful discussions.