Geometry, thermodynamics, and finite-size corrections in the critical Potts model.
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 <N(c)> of the QBCPM has an energy-like singularity for q not equal to 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, <N(b)>, 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.
Hu
C K
CK
Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan. huck@phys.sinica.edu.tw
Chen
J A
JA
Izmailian
N S
NS
Kleban
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P