Abstract
We study the entropy of dimers on a semi-infinite M*N square lattice (N to infinity ) with lattice interaction energy per dimer mu 1 and nearest-neighbour interaction energy mu 2. Numerical computations based on recursive transfer matrices show that for M=1, 2, 3, 4 and 5, and under certain conditions, the constant- mu 2 curves of the entropy as a function of the coverage theta 1 and the fraction theta 2' of the maximum number of possible nearest neighbours, merge into a single curve forming arches that meet at cusps. At the highest points of these arches, the interaction energies are in the ratio of small whole numbers. Based on the analysis of the configurations at the cusps, we extrapolate the results to the infinite two-dimensional lattice (M= infinity ) and obtain the location of at least two cusps. The first cusp occurs at theta 1=1/2, theta 2'=0 and zero entropy, and the second at theta 1=2/3, theta 2'=2/9 and an entropy of 0.102.
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