Thermodynamics of dimers on a rectangular<i>L</i>×<i>M</i>×<i>N</i>lattice

Abstract

The exact closed-form analytic solution of the problem of dimers on infinite two-dimensional and three-dimensional lattices is obtained. Entropy, isothermal compressibility, and constant pressure heat capacity of the system are given in terms of the normalized number density of dimers. The absolute activity of dimers is also given in terms of the normalized number density; it exhibits a behavior near close packing with a critical exponent exactly equal to 2, and with an amplitude 1/(4φ), where φ is the molecular freedom per dimer at close packing.