Building upon his previous work with Scullard (see below), Jesper Lykke Jacobsen shows how to reformulate their graph polynomial method used access to the critical temperature of the q-state Potts model on a general two-dimensional lattice, into an eigenvalue method.
The numerous advantages of this reformulation are discussed and demonstrated by applying the method to three significant, unsolved problems:
- Bond percolation on the kagome lattice.
- Site percolation on the square lattice.
- Self-avoiding polygons (SAPs) on the square lattice
This paper is one from the JPhysA Special Issue: Exactly Solved Models and Beyond produced in honour of R J Baxter’s 75th birthday. It is a further reflection of the ongoing influence of Baxter’s work.
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Jesper Lykke Jacobsen works within the Laboratory of Theoretical Physics at École Normale Supérieure a member of Paris Sciences et Lettres Research University. His research interests include statistical physics, disordered systems, conformal field theory and exactly solvable models.
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This work is licensed under a Creative Commons Attribution 3.0 Unported License. Image: Jesper Lykke Jacobsen 2015 J. Phys. A: Math. Theor. 48 454003 copyright IOP Publishing Ltd 2015