A novel powerful mathematical method is presented, which allows us to find an analytical solution of a simplified version of the statistical multifragmentation model with the restriction that the largest fragment size cannot exceed the finite volume of the system. A complete analysis of the isobaric partition singularities is done for finite system volumes. The finite size effects for large fragments and the role of metastable (unstable) states are discussed. These results allow us, for the first time, to exactly describe the finite volume analog of the bulk nuclear liquid phase and understand completely its contribution to the grand canonical partition.

PACS numbers: 25.70.Pq, 21.65.+f, 24.10.Pa