Percolation of interacting classical dimers on the square lattice

We study the percolation properties of the interacting classical dimer model on the square lattice by means of Monte Carlo simulations and finite-size scaling analysis. We define Ising clusters based on the dimer configuration; the percolation point of the clusters coincides with the critical point of the Kosterlitz–Thouless transition of the dimer model, which is T c = 0.654 ( 2 ) . Furthermore, we find that the largest cluster at the Kosterlitz–Thouless point is a fractal, with fractal dimension D c = 1.874 ( 2 ) , which coincides with the critical exponent describing the critical behavior of the dimer–dimer correlation function, which is theoretically predicted to be 15/8.