The dimer model on the triangular lattice

Abstract

We analyze the partition function of the dimer model on an $\mathcal{M}\times \mathcal{N}$ triangular lattice wrapped on torus obtained by Fendley, Moessner and Sondhi [Phys. Rev. B \textbf{66}, 214513 (2002)]. From a finite-size analysis we have found that the dimer model on such a lattice can be described by conformal field theory having central charge $c=1$. The shift exponent for the specific heat is found to depend on the parity of the number of lattice sites $\mathcal{N}$ along a given lattice axis: e.g., for odd $\mathcal{N}$ we obtain the shift exponent $\lambda =1$, while for even $\mathcal{N}$ it is infinite ($\lambda =\infty$). In the former case, therefore, the finite-size specific-heat pseudocritical point is size dependent, while in the latter case, it coincides with the critical point of the thermodynamic limit.

15 pages, 4 figures

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• Eigenstate thermalization hypothesis in quantum dimer models
• Exact solution of the $2d$ dimer model: Corner free energy, correlation functions and combinatorics
• Finite-size corrections and scaling for the dimer model on the checkerboard lattice
• Exact finite-size corrections for the spanning-tree model under different boundary conditions
• The Pfaffian Sign Theorem for the Dimer Model on a Triangular Lattice
• Finite-size scaling of free energy in the dimer model on a hexagonal domain