Finite-size scaling corrections in two-dimensional Ising and Potts ferromagnets

TL;DR

This paper investigates finite-size scaling corrections in 2D Ising and Potts ferromagnets using numerical methods, revealing lattice-dependent patterns of correction term amplitudes and their potential cancellations.

Contribution

It provides numerical evidence for the vanishing of certain correction amplitudes in specific lattice types and extends understanding of finite-size effects in these models.

Findings

Amplitudes of N^{-2} correction terms are zero for triangular and honeycomb Ising systems.

Results suggest lattice-dependent cancellation patterns in correction amplitudes.

Small non-zero amplitudes for Potts correlation lengths cannot be conclusively ruled out.

Abstract

Finite-size corrections to scaling of critical correlation lengths and free energies of Ising and three-state Potts ferromagnets are analysed by numerical methods, on strips of width $N$ sites of square, triangular and honeycomb lattices. Strong evidence is given that the amplitudes of the ``analytical'' correction terms, $N^{-2}$, are identically zero for triangular-- and honeycomb Ising systems. For Potts spins, our results are broadly consistent with this lattice-dependent pattern of cancellations, though for correlation lengths non-vanishing (albeit rather small) amplitudes cannot be entirely ruled out.