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 Ports 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 energylike singularity for q not equal 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. [S1063-651X(99)09612-9].