Thermodynamics and maximal entropy of a monomer-dimer system on a ladder geometry

Abstract We consider a mixture of dimers and monomers, or defects, on a ladder lattice, with different binding energies, and study the thermodynamics of this system in the canonical ensemble, at a fixed density of monomers. We use Grassmannian techniques in order to construct an effective fermionic action, and evaluate exactly the entropy, specific heat, and correlation functions between monomers and pairs of monomers. We show in particular that, at low temperature, the residual entropy is maximal and equal to the full dimer configurational entropy for a density at which the chemical potential of the monomers is quasi independent of the temperature. The correlation functions present two correlation lengths that explain their oscillatory behavior. The characteristics of the entropy and specific heat are compared with dilute spin-ice systems and discussed.