  We analyze classical dimer models on the square and triangular lattice using
a tensor network representation of the dimers. The correlation functions are
numerically calculated using the recently developed "Tensor renormalization
group" (TRG) technique. The partition function for the dimer problem can be
calculated exactly by the Pfaffian method which is used here as a platform for
comparing the numerical results. TRG turns out to be a powerful tool for
describing gapped systems with exponentially decaying correlations very
efficiently due to its fast convergence. This is the case for the dimer model
on the triangular lattice. However, the convergence becomes very slow and
unstable in case of the square lattice where the model has algebraically
decaying correlations. We highlight these aspects with numerical simulations
and critically appraise the robustness of TRG approach by contrasting the
results for small and large system sizes against the exact calculations.
Furthermore, we benchmark our TRG results with classical Monte Carlo (MC)
method.
