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Plate-Nematic Phase in Three Dimensions.

Margherita Disertori1, Alessandro Giuliani2, Ian Jauslin3

  • 1Institute for Applied Mathematics & Hausdorff Center for Mathematics, University of Bonn, Bonn, Germany.

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|July 18, 2020
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Summary
This summary is machine-generated.

We prove the existence of a uni-axial nematic phase in systems of anisotropic plates. This phase exhibits long-range orientational order without translational order, emerging from hard-core interactions.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Materials Science

Background:

  • Anisotropic particles interacting via hard-core potentials are fundamental in condensed matter physics.
  • Understanding phase transitions, such as the emergence of orientational order, is crucial for predicting material properties.

Purpose of the Study:

  • To rigorously prove the existence of a uni-axial nematic phase in a system of anisotropic plates.
  • To characterize the nature of this phase, specifically its orientational order and lack of translational order.

Main Methods:

  • A coarse-graining procedure was employed to simplify the complex plate interactions.
  • The simplified model was mapped to a contour model for theoretical analysis.
  • Pirogov-Sinai methods were utilized for rigorous control of the contour theory.

Main Results:

  • The existence of a uni-axial nematic phase was proven within a specific range of particle densities.
  • This phase is characterized by long-range alignment of the minor axes of the plates.
  • No long-range translational order was observed in the system.

Conclusions:

  • The study provides a rigorous mathematical framework for understanding the formation of orientational order in systems of anisotropic particles.
  • The findings contribute to the theoretical understanding of phase transitions in soft matter systems.
  • The employed methods offer a pathway for analyzing other complex interacting particle systems.