  In this paper we pursue the use of information measures (in particular,
information diagrams) for the study of entanglement in symmetric multi-quDit
systems. We use generalizations to U(D) of spin U(2) coherent states and their
adaptation to parity (multicomponent Schr\"odinger cats) and we analyse one-
and two-quDit reduced density matrices. We use these correlation measures to
characterize quantum phase transitions occurring in Lipkin-Meshkov-Glick models
of D=3-level identical atoms and we propose the rank of the corresponding
reduced density matrix as a discrete order parameter.
