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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
Summary
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.
- 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.