Abstract
One of the distinctive feature of the QCD phase diagram is the possible emergence of a finite volume transition point as a particular point in the behavior of any thermodynamical response function considered to study the colorless deconfinement phase transition in finite volume. Many properties of this finite volume transition point are considered as an extremely difficult task, even in the simplest known cases. In order to identify and locate the colorless QCD deconfinement finite volume transition point, a new approach using the finite-size cumulant expansion of the order parameter and the L-m,L-n-Method in colorless QCD-thermodynamics was developed. We have shown that cumulants of higher order behave in a particular enough way revealing pronounced oscillations in the transition region. In the context of our model, the finite volume transition point is always associated with the appearance of a particular point in any cumulant under consideration. Consequently, new higher order cumulants are calculated, offering a distinctive method, providing additional information and precision in locating the finite volume transition point. We derive the final expressions of four of them and investigate their behavior and their sign structure in the finite volume transition region.