Correlation Function in Ising Models

TL;DR

This paper uses a cluster algorithm to simulate the Fourier transform of the correlation function in 2D and 3D Ising models, confirming some theoretical predictions and challenging others, with results aligning with series expansions and exact solutions.

Contribution

It demonstrates the effectiveness of a single cluster algorithm with improved estimators for calculating correlation functions in Ising models.

Findings

Simulation results agree with series expansion and exact solutions in 2D.

Data do not support Fisher's hypothesis regarding lattice dependence in 2D.

In 3D, the amplitude ratio f_+/f_- is found to be 2.06(1).

Abstract

We simulated the fourier transform of the correlation function of the Ising model in two and three dimensions using a single cluster algorithm with improved estimators. The simulations are in agreement with series expansion and the available exact results in $d=2$, which shows, that the cluster algorithm can succesfully be applied for correlations. We show as a further result that our data do not support a hypothesis of Fisher that in any $d=2$ lattice the fourier transform of the correlation function depends on the lattice generating function only. In $d=3$ our simulation are again in agreement with the results from the series expansion, except for the amplitudes $f_{\pm}$, where we find $f_+/f_-=2.06(1)$.