Hu CK, Chen JA, Izmailian NS, Kleban P. Geometry, thermodynamics, and finite-size corrections in the critical Potts model.
PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999;
60:6491-5. [PMID:
11970564 DOI:
10.1103/physreve.60.6491]
[Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/22/1999] [Revised: 07/06/1999] [Indexed: 04/18/2023]
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 <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.
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