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

Minghui Hu1, Chao Zhang1, Dajun Zhang1

  • 1Anhui Normal University, Department of Physics and Anhui Province Key Laboratory for Control and Applications of Optoelectronic Information Materials, Wuhu, Anhui 241000, China.

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|June 26, 2026
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Summary

This study introduces a novel quasi-two-dimensional XY model where long-range spin order emerges, challenging conventional physics. The research demonstrates a new pathway for stabilizing order in low-dimensional systems.

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Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Low-Dimensional Systems

Background:

  • The Mermin-Wagner theorem traditionally prohibits long-range order in 2D systems with continuous symmetries.
  • Existing paradigms assert limitations on ordering in quasi-two-dimensional (q2D) systems with short-range (SR) interactions.
  • Understanding spin phases in q2D models is crucial for various physics subfields.

Purpose of the Study:

  • To investigate a strictly SR q2D XY model with a unique intersecting plane geometry.
  • To determine the phase diagram and identify conditions for emergent long-range (LR) order.
  • To explore the nature of this emergent order and its associated physics.

Main Methods:

  • Large-scale Monte Carlo simulations.
  • Finite-size scaling analysis.
  • Theoretical modeling of spin interactions on intersecting planes.

Main Results:

  • A complete phase diagram was established for the proposed q2D XY model.
  • A LR ordered phase emerges when spins on intersecting planes exhibit Berezinskii-Kosterlitz-Thouless critical behavior.
  • The emergent LR order is anisotropic, with true LR correlations along intersection lines and quasi-LR order perpendicularly.

Conclusions:

  • The study reveals a novel mechanism for stabilizing LR spin order in low-dimensional systems with continuous symmetries.
  • The findings challenge conventional understanding based on the Mermin-Wagner theorem.
  • The proposed model offers a new platform for studying exotic superfluidity and related phenomena.