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Updated: Apr 25, 2026
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Orientational Transition in a Liquid Crystal Triggered by the Thermodynamic Growth of Interfacial Wetting Sheets
Published on: May 15, 2017
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Topological phase transition in a discrete quasicrystal
1Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel.
Summary
This study reveals a hidden continuous symmetry in a discrete tiling model, leading to a topological phase transition. Vortex proliferation drives this transition from order to disorder in quasicrystalline systems.
Area of Science:
- Condensed Matter Physics
- Materials Science
- Statistical Mechanics
Background:
- Two-dimensional tiling models exhibit complex ordering.
- Quasicrystalline states possess unique symmetries and properties.
- Understanding phase transitions is crucial for materials science.
Purpose of the Study:
- Investigate a two-dimensional tiling model with discrete degrees of freedom.
- Explore the implications of hidden continuous global symmetry in the infinite lattice limit.
- Characterize the topological phase transition driven by vortex proliferation.
Main Methods:
- Analysis of a two-dimensional tiling model.
- Identification of hidden continuous global symmetry.
- Study of Goldstone modes as quasicrystalline phasonic degrees of freedom.
- Investigation of vortex proliferation and topological phase transitions.
Main Results:
- A discrete tiling model possesses a hidden continuous global symmetry.
- Goldstone modes correspond to quasicrystalline phasonic degrees of freedom.
- A topological phase transition from quasi-long-range order to a disordered phase occurs at finite temperature.
- Vortex proliferation drives this transition.
Conclusions:
- The discrete nature of the model belies its continuous symmetry.
- Topological phase transitions can occur in systems with apparent discrete degrees of freedom.
- Results suggest universality for 2D systems with quasicrystalline ground states.
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