CONICET | Buscador de Institutos y Recursos Humanos

We perform an analytical study of a simplified bipartite matching problem inwhich there exists a constant matching energy, and both heterosexual and homosexual pairingsare allowed. We obtain the partition function in a closed analytical form and we calculatethe corresponding thermodynamic functions of this model. We conclude that the modelis favored at high temperatures, for which the probabilities of heterosexual and homosexualpairs tend to become equal. In the limits of low and high temperatures, the system isextensive, however this property is lost in the general case. There exists a relation betweenthe matching energies for which the system becomes more stable under external (thermal)perturbations. As the difference of energies between the two possible matches increases thesystem becomes more ordered, while the maximum of entropy is achieved when these energiesare equal. In this limit, there is a first order phase transition between two phases withconstant entropy.