  We study the finite-size effects on the deconfinement phase transition (DPT)
of hot and / or dense hadronic matter, using a simple thermodynamic model based
on the assumption of coexistence of confined and deconfined phases in a finite
volume, with the two-phases matter Equations of State. For the QGP, we consider
a partition function (PF) with the exact color-singletness requirement. A
problem arises in the limit of small QGP volumes when using the usual
color-singlet partition function (CSPF) derived in the saddle point
approximation. To avoid the problem, we have then proposed a method for
calculating a suitable CSPF, which allows us to accurately calculate physical
quantities describing well the DPT at finite volumes. We show that in the limit
of infinite volume, these thermodynamic quantities exhibit a discontinuity at a
critical point Tc(infinity) (or muc(infinity)). In a finite size system, all
singularities are smoothed out over a broadened critical region, shifted from
the critical point position in the thermodynamic limit. The first derivatives
of these thermodynamic quantities show delta function singularities at the
critical point in the thermodynamic limit, while in a finite volume, these
delta singularities are smeared into finite peaks of widths deltaT(V) (or
deltamu(V)), with the maxima of the peaks occuring at pseudo-critical points
Tc(V) (or muc(V)). An analysis of the finite size scaling behavior at
criticality of these maxima as well as of the width of the transition region
and the shift of the critical point allows us to determine the critical
exponents characterizing the DPT. Our results are in good agreement with those
predicted by other studies for a first-order phase transition.
