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Geometry, thermodynamics, and finite-size corrections in the critical Potts model

Chin-Kun Hu·Jau-Ann Chen·N. Sh. Izmailian·P. Kleban
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Abstract

We establish an intriguing connection between geometry and thermodynamics in the critical q-state Potts model on two-dimensional lattices, using the q-state bond-correlated percolation model (QBCPM) representation. We find that the number of clusters of the QBCPM has an energy-like singularity for q different from 1, which is reached and supported by exact results, numerical simulation, and scaling arguments. We also establish that the finite-size correction to the number of bonds, has no constant term and explains the divergence of related quantities as q --> 4, the multicritical point. Similar analyses are applicable to a variety of other systems.

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Chin-Kun Hu, Jau-Ann Chen, N. Sh. Izmailian, P. Kleban. 2000-01-07. Geometry, thermodynamics, and finite-size corrections in the critical Potts model. https://doi.org/10.1103/physreve.60.6491

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