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

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

1999-05-14

arxiv.org/abs/cond-mat/9905203v2

Phys. Rev. E 60, 6491 (1999)

Physics

Condensed Matter

Statistical Mechanics

12 pages, 6 figures

Scientific paper

10.1103/PhysRevE.60.6491

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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