2007/05/31 by Fabien Trousselet, F. Trousselet, Pierre Pujol +5
Materials Science · Mathematics · Physics and Astronomy · #Anisotropy #Antiferromagnetism #Condensed matter physics #Criticality #Diagonal #Dimer #Geometry #Hexagonal lattice #Interaction energy #Isotropy #Lattice (music) #Material Dynamics and Properties #Mathematics #Molecule #Phase transition #Physics #Quantum mechanics #Square lattice #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Transfer matrix #cond-mat.stat-mech #cond-mat.str-el
paper · pdf · doi:10.1103/physreve.76.041125
published as PRE 76, 041125 (2007) · 12 pages, 16 figures
arxiv created 2007/05/31 · openalex publication_date 2007/10/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.