Long-range Order in a Short-range Quasi-2D XY Model

TL;DR

This study uses large-scale simulations to reveal a long-range ordered phase in a quasi-2D XY model with short-range interactions, characterized by anisotropic correlations and Goldstone modes, expanding understanding of low-dimensional superfluid order.

Contribution

It introduces a novel Q2D XY model with finite short-range couplings and demonstrates the emergence of long-range order and anisotropic correlations through comprehensive Monte Carlo simulations.

Findings

Long-range order appears in the Q2D XY model.

Order is anisotropic, with correlations along and perpendicular to intersection lines.

The phase exhibits Goldstone-mode physics.

Abstract

The phase of spins in the quasi-two-dimensional (Q2D) XY model has emerged as a topic of significant interest across multiple physics subfields. Here, we propose a short-range (SR) Q2D XY model defined on a plane perpendicularly intersected by a group of parallel planes, with each plane consisting of nearest-neighbor-coupled XY spins. We perform large-scale Monte Carlo simulations to establish the full phase diagram of the Q2D XY model, aided by finite-size scaling. A long-range (LR) ordered phase emerges in the Q2D model when the spins on the parallel planes develop a Berezinskii-Kosterlitz-Thouless critical phase. In the LR ordered phase, ordering is anisotropic: LR correlations develop along the direction of the intersection lines, while critical correlations emerge perpendicular to them. Furthermore, the LR ordered phase exhibits Goldstone-mode physics. Our study hence reveals the existence of LR order in a Q2D XY model with finite SR couplings and opens up a new avenue to explore superfluid orders in low dimensions.