High-accuracy estimates of the critical parameters for the XY model on the square and the triangular lattices using the high-temperature expansions

The high-temperature expansions of 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. We determine βc=0.5599(7) and σ=0.499(5) in the case of the square lattice. For the triangular lattice case, we estimate βc=0.3412(4) and σ=0.500(5).