We study quantum spin systems described by Heisenberg-like models at finite
temperature with a strict site-occupation constraint imposed by a procedure
originally proposed by V. N. Popov and S. A. Fedotov \cite{Popov-88}. We show
that the strict site-occupation constraint modifies quantitatively the
behaviour of physical quantities when compared to the case for which this
constraint is fixed in the average by means of a Lagrange multiplier method.
The relevance of the N\'eel state with the strict site-occupation contraint of
the spin lattice is studied. With an exact site-occupation the transition
temperature of the antiferromagnetic N\'eel and spin liquid order parameters
are twice as large as the critical temperature one gets with an average
Lagrange multiplier method. We consider also a mapping of the low-energy spin
Hamiltonian into a QED3​ Lagrangian of spinons. In this framework we compare
the dynamically generated mass to the one obtained by means of an average
site-occupation constraint.Comment: PhD Thesis, 137 pages, 18 figure