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Classical dimer model with anisotropic interactions on the square lattice.

Hiromi Otsuka1

  • 1Department of Physics, Tokyo Metropolitan University, Tokyo 192-0397, Japan.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 8, 2009
PubMed
Summary
This summary is machine-generated.

This study explores phase transitions in a classical dimer model. Anisotropy drives Berezinskii-Kosterlitz-Thouless transitions, and numerical methods reveal the global phase diagram, including repulsion phase boundaries.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Phase Transitions

Background:

  • Classical dimer models on lattices are crucial for understanding emergent phenomena.
  • Anisotropic interactions introduce complexity, influencing phase behavior and transition mechanisms.

Purpose of the Study:

  • To investigate phase transitions and map the phase diagram of a classical dimer model with anisotropic interactions on a square lattice.
  • To establish criteria for determining transition points and universal level-splitting conditions based on existing theoretical frameworks.
  • To elucidate the properties of distinct phases, particularly the strong repulsion phase.

Main Methods:

  • Numerical diagonalization of nonsymmetric real transfer matrices up to linear dimension L=20.
  • Analysis of the orientational order parameter and its response to anisotropic perturbations.
  • Examination of the dispersion relation for one-string motion in the strong repulsion limit.

Main Results:

  • Identified Berezinskii-Kosterlitz-Thouless transitions from dimer-liquid to columnar phases in the attractive region.
  • Determined the global phase diagram, including the boundary between dimer-liquid and strong repulsion phases.
  • Observed a twofold "zero-energy flat band" in the one-string motion dispersion relation for the strong repulsion phase.

Conclusions:

  • Anisotropy plays a key role in driving phase transitions in the classical dimer model.
  • Numerical diagonalization provides an effective method for mapping complex phase diagrams.
  • The "zero-energy flat band" offers an intuitive explanation for the behavior of the strong repulsion phase.