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Self-assembly of Complex Two-dimensional Shapes from Single-stranded DNA Tiles
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Published on: May 8, 2015

Semiflexible fully packed loop model and interacting rhombus tilings.

Jesper Lykke Jacobsen1, Fabien Alet

  • 1Laboratoire de Physique Théorique de l'Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris, France.

Physical Review Letters
|April 28, 2009
PubMed
Summary
This summary is machine-generated.

This study analyzes rhombi tilings with repulsive interactions, revealing critical exponents that change with interaction strength. The model predicts a Kosterlitz-Thouless transition to an ordered phase around 110 K.

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Area of Science:

  • Statistical mechanics
  • Condensed matter physics
  • Mathematical physics

Background:

  • Recent adsorption experiments provide motivation.
  • The study focuses on tilings of the plane using three rhombus types.
  • An interaction disfavors adjacent rhombi of the same type.

Purpose of the Study:

  • To investigate a specific tiling model with repulsive interactions.
  • To connect this model to fully packed loop systems.
  • To analyze critical exponents and phase transitions.

Main Methods:

  • Utilizing Coulomb gas techniques to solve the model.
  • Analyzing the behavior of critical exponents with varying interaction strength.
  • Predicting phase transitions based on theoretical calculations.

Main Results:

  • The critical exponents vary continuously with interaction strength.
  • The model exhibits a Kosterlitz-Thouless transition at low temperatures.
  • A transition to an ordered phase is predicted around 110 K.

Conclusions:

  • The model provides insights into statistical mechanics of tilings.
  • The findings are relevant to understanding phase transitions in related systems.
  • The theoretical predictions can be experimentally verified.