Criticality of a classical dimer model on the triangular lattice

F. Trousselet, P. Pujol, F. Alet, and D. Poilblanc
Phys. Rev. E 76, 041125 – Published 19 October 2007

Abstract

We consider a classical interacting dimer model which interpolates between the square lattice case and the triangular lattice case by tuning a chemical potential in the diagonal bonds. The interaction energy simply corresponds to the number of plaquettes with parallel dimers. Using transfer matrix calculations, we find in the anisotropic triangular case a succession of different physical phases as the interaction strength is increased: a short-range disordered liquid dimer phase at low interactions, then a critical phase similar to the one found for the square lattice, and finally a transition to an ordered columnar phase for large interactions. Our results indicate that criticality and nonbipartiteness are compatible in a dimer model. For the isotropic triangular case, we have indications that the system undergoes a first-order phase transition to an ordered phase, without appearance of an intermediate critical phase.

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  • Received 1 June 2007

DOI:https://doi.org/10.1103/PhysRevE.76.041125

©2007 American Physical Society

Authors & Affiliations

F. Trousselet, P. Pujol, F. Alet, and D. Poilblanc

  • Laboratoire de Physique Théorique, CNRS, Université Paul Sabatier, 31062 Toulouse, France

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Issue

Vol. 76, Iss. 4 — October 2007

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