Long-Range Order in a Strictly Short-Range Quasi-2D XY Model: When Critical Fluctuations Matter

Abstract

The phase of spins in the quasi-two-dimensional (q2D) XY model has emerged as a topic of significant interest across multiple subfields of physics. Conventional wisdom, rooted in the Mermin-Wagner theorem and supported by existing paradigms, asserts that true long-range (LR) order is prohibited in q2D systems with continuous symmetries and short-range (SR) interactions. In this Letter, we propose a strictly SR q2D XY model defined on a plane perpendicularly intersected by a group of parallel planes, where each plane consists of XY spins coupled via nearest-neighbor interactions. Through large-scale Monte Carlo simulations complemented by finite-size scaling analysis, we establish the complete phase diagram of the setup. A LR ordered phase emerges in the q2D model when the spins on the parallel planes develop a Berezinskii-Kosterlitz-Thouless critical phase. The LR ordered phase is anisotropic: true LR correlations develop exclusively along the direction of the intersection lines, while the perpendicular direction exhibits quasi-long-range order. Furthermore, the LR order exhibits Goldstone-mode physics. Our findings reveal a mechanism for stabilizing LR order in low-dimensional systems with continuous symmetries, thereby establishing a new platform for studying exotic superfluidity.