Thermodynamics and molecular freedom of dimers on plane triangular lattices

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Abstract
This is an extension of three previous papers dealing with dimers on rectangular lattices (one, two, and three dimensions). The technique presented in the first paper in this series continues to be fruitful for dimers on plane triangular lattices. Entropy, isothermal compressibility, constant pressure heat capacity, and molecular freedom per dimer at close packing are obtained exactly for lattices infinite in one direction and finite in the other. Observations made in the third paper of the series concerning molecular freedom per dimer at close packing on rectangular lattices are used to extrapolate our results to infinite plane triangular lattices. At close packing, the molecular freedom per dimer on an infinite plane triangular lattice is calculated to be 2.356 527... in agreement with the value obtained by Nagle. Based on our earlier findings, the value of 2.356 527... was used to obtain the analytic fit for the thermodynamic quantities in terms of the normalized number density.