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Interacting classical dimers on the square lattice.

Fabien Alet1, Jesper Lykke Jacobsen, Grégoire Misguich

  • 1Service de Physique Théorique (URA 2306 of CNRS), CEA Saclay, 91191 Gif sur Yvette, France.

Physical Review Letters
|August 11, 2005
PubMed
Summary
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This study reveals a Kosterlitz-Thouless transition in a dimer model, moving from an ordered low-temperature phase to a critical high-temperature phase. This provides insights into quantum dimer models and their phase diagrams.

Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Quantum Magnetism

Background:

  • The study investigates a model of close-packed dimers on a square lattice, relevant to the classical limit of quantum dimer models.
  • Nearest neighbor interactions between parallel dimers are considered, building upon foundational work in the field.

Purpose of the Study:

  • To analyze the phase transitions and critical behavior of the dimer model.
  • To understand the connection between classical dimer models and quantum dimer models.
  • To explore the implications for finite-temperature phase diagrams of quantum dimer models.

Main Methods:

  • Monte Carlo simulations were employed to study the system's behavior.
  • Transfer matrix calculations were utilized for precise analysis.

Related Experiment Videos

  • A Coulomb gas model was constructed and its coupling constant numerically computed.

    • Main Results:

    • A Kosterlitz-Thouless transition was identified, separating distinct low- and high-temperature phases.
    • The low-temperature phase exhibits ordered dimer alignment in columns.
    • The high-temperature phase is critical, characterized by continuously varying exponents.

    Conclusions:

    • The Kosterlitz-Thouless transition is a key feature of this dimer model.
    • The Coulomb gas analogy provides a theoretical framework for understanding the observed transition.
    • The findings offer valuable insights into the complex phase diagrams of quantum dimer models, including doped scenarios.