Entropies of the Classical Dimer Model

Biological processes often involve the attachment and detachment of extended molecules to substrates. Here, the classical dimer model is used to investigate these geometric effects on the free energy, which governs both the equilibrium state and the reaction dynamics. We present a simplified version of Fisher’s derivation of the partition function of a two-dimensional dimer model at filling factor $\nu =1$, which takes into account the blocking of two adjacent sites by each dimer. Physical consequences of the dimer geometry on the entropy that are not reflected in simpler theories are identified. Specifically, for dimers adsorbing on the DNA double helix, the dimer geometry gives a persistently nonzero entropy and there is a significant charge inversion as the force binding the particles to the lattice increases relative to the thermal energy, which is not true of the simple lattice gas model for the dimers, in which all the sites are independent.