  We study the finite-size effects for the thermal QCD Deconfinement Phase
Transition (DPT), and use a numerical finite size scaling analysis to extract
the scaling exponents characterizing its scaling behavior when approaching the
thermodynamic limit. For this, we use a simple model of coexistence of hadronic
gas and color-singlet Quark Gluon Plasma (QGP) phases in a finite volume. The
Color-Singlet Partition Function (CSPF) of the QGP cannot be exactly calculated
and is usually derived within the saddle point approximation. When we try to do
calculations with such an approximate CSPF, a problem arises in the limit of
small temperatures and/or volumes (VT3<<1), requiring then additional
approximations if we want to carry out calculations. We propose in this work a
new method for an accurate calculation of any quantity of the finite system,
without explicitly calculating the CSPF itself and without any approximation.
By probing the behavior of some useful thermodynamic response functions on the
hole range of temperature, it turns out that in a finite size system, all
singularities in the thermodynamic limit are smeared out and the transition
point is shifted away. A numerical finite size scaling analysis of the obtained
data allows us to determine the scaling exponents of the QCD DPT. Our results
expressing the equality between their values and the space dimensionality is a
consequence of the singularity characterizing a first order phase transition
and agree very well with the predictions of other FSS theoretical approaches
and with the results of both lattice QCD and Monte Carlo models calculations.
