High-temperature expansion of the magnetic susceptibility and higher moments of the correlation function for the two-dimensional XY model

TL;DR

This paper computes high-temperature series for the 2D XY model's magnetic susceptibility and correlation moments, estimating critical parameters and confirming theoretical predictions with high precision.

Contribution

It extends the high-temperature series to order 33 using an improved finite lattice method, providing precise estimates of critical temperature and correction exponents.

Findings

Estimated inverse critical temperature as β_c=1.1200(1)

Determined the correction exponent θ=0.054(10)

Results agree with renormalization group predictions

Abstract

We calculate the high-temperature series of the magnetic susceptibility and the second and fourth moments of the correlation function for the XY model on the square lattice to order $\beta^{33}$ by applying the improved algorithm of the finite lattice method. The long series allow us to estimate the inverse critical temperature as $\beta_c=1.1200(1)$, which is consistent with the most precise value given previously by the Monte Carlo simulation. The critical exponent for the multiplicative logarithmic correction is evaluated to be $\theta=0.054(10)$, which is consistent with the renormalization group prediction of $\theta={1/16}$.