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Related Experiment Videos

Classical dimers with aligning interactions on the square lattice.

Fabien Alet1, Yacine Ikhlef, Jesper Lykke Jacobsen

  • 1Laboratoire de Physique Théorique, UMR CNRS 5152, Université Paul Sabatier, 31062 Toulouse, France. alet@irsamc.ups-tlse.fr

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 13, 2006
PubMed
Summary

We studied dimers on a square lattice, finding a crystal melts into a critical phase via a Kosterlitz-Thouless transition. Adding monomers creates a new critical line in the Ashkin-Teller universality class.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Phase Transitions

Background:

  • The study focuses on close-packed dimers on a square lattice, a system exhibiting complex phase behavior.
  • Nearest-neighbor dimer interactions favor parallel alignment, leading to a crystalline phase at low temperatures.

Purpose of the Study:

  • To investigate the phase transitions and critical phenomena in a dimer model with nearest-neighbor interactions.
  • To analyze the effect of introducing monomers on the system's critical behavior.
  • To provide a theoretical interpretation using a Coulomb gas mapping and explore analytic results for noninteracting dimers.

Main Methods:

  • Large-scale Monte Carlo simulations and transfer matrix calculations were employed.
  • The system was mapped to a Coulomb gas model for theoretical interpretation.

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  • Numerical calculations determined coupling constants and exponents with high precision.
  • Analytic methods including Bethe ansatz and free field analysis were used for the noninteracting case.

    • Main Results:

    • A Kosterlitz-Thouless phase transition was identified, melting the crystal into a high-temperature critical phase with continuously varying exponents.
    • The introduction of monomers led to a new critical line within the Ashkin-Teller universality class.
    • A tricritical point was found at finite temperature and monomer fugacity.
    • Analytic results for noninteracting dimer coverings were derived.

    Conclusions:

    • The dimer model exhibits rich phase behavior driven by interactions and monomer introduction.
    • The Kosterlitz-Thouless transition and Ashkin-Teller universality class are key to understanding the system's critical properties.
    • The Coulomb gas mapping provides a powerful theoretical framework for analyzing such systems.