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

1999/05/31 by Chin-Kun Hu, Chin‐Kun Hu, Jau-Ann Chen +3 · 3 citations
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Connection (principal bundle) #Critical exponent #Critical point (mathematics) #Exponent #Geometry #Ising model #Mathematical physics #Mathematics #Percolation (cognitive psychology) #Physics #Potts model #Scaling #Singularity #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Thermodynamics #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.60.6491

published as Phys. Rev. E 60, 6491 (1999) · 12 pages, 6 figures

openalex publication_date 1999/12/01 · arxiv created 2000/01/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Cluster analysis and finite-size scaling for Ising spin systems

Cited by

• Exact finite-size-scaling corrections to the critical two-dimensional Ising model on a torus
• Homology of Fortuin–Kasteleyn Clusters of Potts Models on the Torus
• Exact finite-size-scaling corrections to the critical two-dimensional Ising model on a torus: II. Triangular and hexagonal lattices