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

TL;DR

This paper uncovers a deep link between geometry and thermodynamics in the critical q-state Potts model, revealing finite-size effects and singularities through exact, numerical, and scaling methods.

Contribution

It introduces a novel connection between geometric cluster properties and thermodynamic singularities in the critical Potts model, supported by multiple analytical approaches.

Findings

Number of clusters exhibits an energy-like singularity for q ≠ 1

Finite-size correction to the number of bonds has no constant term

Divergence of quantities as q approaches 4, the multicritical point

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 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.