Numerical investigation of logarithmic corrections in two-dimensional spin models

TL;DR

This paper investigates logarithmic corrections in the decay of correlation functions at criticality in various two-dimensional spin models using Monte Carlo simulations and conformal mapping techniques.

Contribution

It provides a numerical analysis of logarithmic corrections in 2D spin models, demonstrating the mutual consistency of leading and correction terms.

Findings

Logarithmic corrections significantly affect the decay of correlations.

Numerical results align with theoretical expectations of correction terms.

Conformal mapping effectively relates finite and infinite geometries.

Abstract

The analysis of correlation function data obtained by Monte Carlo simulations of the two-dimensional 4-state Potts model, XY model, and self-dual disordered Ising model at criticality are presented. We study the logarithmic corrections to the algebraic decay exhibited in these models. A conformal mapping is used to relate the finite-geometry information to that of the infinite plane. Extraction of the leading singularity is altered by the expected logarithmic corrections, and we show numerically that both leading and correction terms are mutually consistent.