  The influence of Franco Iachello in Physics during the last 50 years and, in
particular, in the use of algebraic methods applied to very different physical
problems has been broad, extense and have permeated most branches of Physics,
from Nuclear and Molecular to Particle and Condensed Matter physics. Apart of
many other contributions, at the beginning of the 2000's he introduced the
concept of critical point symmetry and triggered the study of the many faces of
quantum phase transitions in nuclei and other mesoscopic systems. In this
contribution, we present the analysis of the scaling properties of the Lipkin
model spectrum at the phase transition point and we focus on the differences
between first and second order quantum phase transitions. Moreover, we explain
how the obtained results can be also of application for the interacting boson
model.
