The dimer model on the triangular lattice

TL;DR

This paper studies the dimer model on a triangular lattice, revealing its conformal field theory description with central charge c=1 and how finite-size effects depend on lattice parity.

Contribution

It provides a finite-size analysis of the dimer model on a triangular lattice, connecting it to conformal field theory and uncovering parity-dependent shift exponents.

Findings

Dimer model on triangular lattice described by conformal field theory with c=1

Shift exponent for specific heat depends on lattice site parity

Finite-size specific-heat pseudocritical point behavior varies with parity

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.