Crossover and Critical Behavior in the Layered XY Model

TL;DR

This study uses Monte Carlo simulations to explore how layered XY models transition from 2D topological to 3D critical behavior, revealing a logarithmic scaling of the critical temperature with anisotropy and the persistence of topological features up to large system sizes.

Contribution

It provides the first detailed analysis of the crossover from quasi-2D to 3D critical behavior in the anisotropic XY model, especially at very small anisotropy values.

Findings

Critical temperature scales logarithmically with anisotropy.

Topological scaling signatures persist up to large system sizes.

Genuine 3D symmetry-breaking emerges only at very large sizes.

Abstract

Motivated by the interplay between 2D and 3D scaling signatures observed in unconventional layered superconductors, we present a systematic Monte Carlo study of the three-dimensional classical XY model with anisotropic in-plane $J_\parallel$ and inter-plane $J_\perp$ couplings. Our study includes very small values of the system anisotropy $\Delta=J_\perp /J_\parallel$ not studied before, and focuses on characterizing the crossover from quasi-2D topological scaling to genuine 3D critical behavior. The numerical results for the critical temperature unambiguously reveal a logarithmic scaling with $\Delta$, directly related to the topological scaling in the 2D limit. Despite the 3D nature of the layered XY criticality, topological scaling signatures survive up to system sizes comparable to the crossover length $\ell_J$, which diverges at small $\Delta$ with a scaling behavior reminiscent of the Berezinskii-Kosterlitz-Thouless (BKT) transition. This shows that genuine 3D symmetry-breaking behavior emerges only at exceedingly large system sizes when the anisotropy is very strong. Our results indicate that new experimental evidence is required to clarify the extent to which the critical signatures observed in layered strongly correlated materials are shaped by their pronounced anisotropy.