Universal scaling function for the two-dimensional Ising model in an external field: A pragmatic approach

TL;DR

This paper introduces a practical, accurate functional form for the spin-spin correlation function of the 2D Ising model across various temperatures and magnetic fields, validated by simulations, with applications in membrane biophysics.

Contribution

The authors propose a new effective functional form for the 2D Ising model's correlation function that works for arbitrary fields and temperatures, validated by simulations.

Findings

High-precision correlation function form validated against simulations.

Analytic corrections to scaling improve accuracy.

Potential application in membrane heterogeneity analysis.

Abstract

We report an effective functional form for the spin-spin correlation function of the 2D Ising model as a function of temperature and field. Although the Ising model has been well studied, no analytical result for the spin-spin correlation function exists for arbitrary magnetic fields and temperatures. We show the validity of our form by comparison with simulations using the Wolff algorithm, and obtain remarkable precision by including analytic corrections to scaling. Given recent interest in comparing biomembrane heterogeneity to Ising criticality, our spin-spin correlation function may be used as a predictive quantitative measure for FRET or NMR membrane experiments.