  We present results of the Monte-Carlo simulations for scaling of the free
energy in dimers on the hexagonal lattice. The traditional Markov-chain
Metropolis algorithm and more novel non-Markov Wang-Landau algorithm are
applied. We compare the calculated results with the theoretical prediction for
the equilateral hexagon and show that the latter algorithm gives more precise
results for the dimer model. For a non-hexagonal domain the theoretical results
are not available, so we present the numerical results for a certain geometry
of the domain. We also study the two-point correlation function in simulations
of dimers and the six-vertex model. The logarithmic dependence of the
correlation function on the distance, which is in accordance with the Gaussian
free field description of fluctuations, is obtained.
