Exact Finite Method of Lattice Statistics. III. Dimers on the Square Lattice

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Abstract
The 2‐dimensional square‐lattice model of hard dimeric molecules has been studied over the entire range of dimer densities. The effects of an external field have been included by allowing different activities for the two possible molecular orientations. Thermodynamic properties have been obtained by the transfer matrix technique for lattices of increasing finite circumference and infinite length. The convergence with increasing size has been the most rapid of all systems yet studied by this technique, satisfactory convergence usually being realized with a circumference of only ten sites. The results are in agreement with previous zero‐field studies employing other methods. There is no phase transition in the presence or absence of an external field, and the equation of state is remarkably insensitive to the field. The limited information obtained regarding the nature of the approach to the close‐packed limit is consistent with recent predictions based on the series method.