TEST OF FINITE-SIZE SCALING PREDICTIONS IN 3 DIMENSIONS

A constrained monomer-dimer (CMD) Model on decorated hypercubic lattices, which is exactly solvable in any dimensionality d, is studied. The model is critical in the limit of maximal packing of the dimer configurations allowed by the constraint. For d = 2 it is equivalent to the rooted-tree model on the square lattice considered by Duplantier and David. The validity of two finite-size scaling predictions in higher dimensionalities is studied: (i) the existence of logarithmic corrections in the free energy due to comers, and (ii) the amplitude-exponent relation for the pair correlation function. The logarithmic finite-size corrections are obtained for arbitrary d, for boundary conditions which are periodic for d' greater-than-or-equal-to 0 dimensions and free in the remaining d - d' dimensions. Dimer-dimer correlation functions are studied at d = 3 for a system finite in two dimensions and infinite in the third. It is shown that the amplitude-exponent relation for the CMD model holds for d = 2 and breaks down for d = 3.