Corner Exponents in the Two-Dimensional Potts Model

TL;DR

This paper investigates the critical behavior at corners in 2D Ising and Potts models using transfer operator methods, confirming conformal invariance predictions with effective angles in anisotropic systems.

Contribution

It provides numerical estimates of local critical exponents at corners for different angles, incorporating anisotropy effects, and compares results with conformal invariance theory.

Findings

Critical exponents match conformal invariance predictions with effective angles.

Finite-size scaling yields consistent local exponents for various angles.

Anisotropic couplings require angle adjustments to match theoretical expectations.

Abstract

The critical behavior at a corner in two-dimensional Ising and three-state Potts models is studied numerically on the square lattice using transfer operator techniques. The local critical exponents for the magnetization and the energy density for various opening angles are deduced from finite-size scaling results at the critical point for isotropic or anisotropic couplings. The scaling dimensions compare quite well with the values expected from conformal invariance, provided the opening angle is replaced by an effective one in anisotropic systems.