  We study the effect of site occupation in 2d quantum spin systems at finite
temperature in a $\pi$-flux state description at the mean-field level. We
impose each lattice site to be occupied by a single SU(2) spin. This is
realized by means of a specific prescription. We consider the low-energy
Hamiltonian which is mapped into a $QED_3$ Lagrangian of spinons. We compare
the dynamically generated mass to the one obtained by means of an average site
occupation constraint.
