Extended scaling behavior of the spatially-anisotropic classical XY model in the crossover from three to two dimensions

TL;DR

This paper extends high-temperature series expansions for the anisotropic 3D XY model to analyze critical behavior and crossover from three to two dimensions, confirming generalized scaling theory predictions.

Contribution

It provides extended series data and numerical analysis of the anisotropic XY model, enhancing understanding of critical temperature and universality in dimensional crossover.

Findings

Critical temperature accurately determined as a function of anisotropy R.

Universality of critical exponents confirmed across different R values.

Scaling theory predictions for 3D to 2D crossover are supported by data.

Abstract

The bivariate high-temperature expansion of the spin-spin correlation-function of the three-dimensional classical XY (planar rotator) model, with spatially-anisotropic nearest-neighbor couplings, is extended from the 10th through the 21st order. The computation is carried out for the simple-cubic lattice, in the absence of magnetic field, in the case in which the coupling strength along the z-axis of the lattice is different from those along the x- and the y-axes. It is then possible to determine accurately the critical temperature as function of the parameter R which characterizes the coupling anisotropy and to check numerically the universality, with respect to R, of the critical exponents of the three-dimensional anisotropic system. The analysis of our data also shows that the main predictions of the generalized scaling theory for the crossover from the three-dimensional to the two-dimensional critical behavior are compatible with the series extrapolations.