Further extensions of the high-temperature expansions for the two-dimensional classical XY model on the triangular and the square lattices

TL;DR

This paper extends high-temperature series expansions for the 2D classical XY model on square and triangular lattices, improving estimates of critical parameters by adding higher-order terms.

Contribution

It provides additional terms in the high-temperature expansions for both lattices, enhancing the precision of critical parameter estimates.

Findings

Extended series to higher orders for both lattices.

Improved estimates of critical parameters.

Enhanced understanding of phase transition behavior.

Abstract

The high-temperature expansions for the spin-spin correlation function of the two-dimensional classical XY (planar rotator) model are extended by two terms, from order 24 through order 26, in the case of the square lattice, and by five terms, from order 15 through order 20, in the case of the triangular lattice. The data are analyzed to improve the current estimates of the critical parameters of the models.