Interacting classical dimers on the square lattice

Fabien Alet 1, Jesper Lykke Jacobsen 1, 2, Gregoire Misguich 1, Vincent Pasquier 1, Frederic Mila 3, Matthias Troyer 4

Physical Review Letters 94 (2005) 235702

We study a model of close-packed dimers on the square lattice with a nearest neighbor interaction between parallel dimers. This model corresponds to the classical limit of quantum dimer models [D.S. Rokhsar and S.A. Kivelson, Phys. Rev. Lett.{\\bf 61}, 2376 (1988)]. By means of Monte Carlo and Transfer Matrix calculations, we show that this system undergoes a Kosterlitz-Thouless transition separating a low temperature ordered phase where dimers are aligned in columns from a high temperature critical phase with continuously varying exponents. This is understood by constructing the corresponding Coulomb gas, whose coupling constant is computed numerically. We also discuss doped models and implications on the finite-temperature phase diagram of quantum dimer models.

  • 1. Service de Physique Théorique (SPhT),
    CNRS : URA2306 – CEA : DSM/SPHT
  • 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud
  • 3. Institute of Theoretical Physics,
    École Polytechnique Fédérale de Lausanne
  • 4. Theoretische Physik,
    ETH Zurich