  We present results obtained from a set of cosmological hydrodynamic
simulations of galaxy clusters, aimed at comparing predictions with
observational data on the diversity between cool-core (CC) and non-cool-core
(NCC) clusters. Our simulations include the effects of stellar and AGN feedback
and are based on an improved version of the smoothed particle hydrodynamics
code GADGET-3, which ameliorates gas mixing and better captures gas-dynamical
instabilities by including a suitable artificial thermal diffusion. In this
Letter, we focus our analysis on the entropy profiles, the primary diagnostic
we used to classify the degree of cool-coreness of clusters, and on the iron
profiles. In keeping with observations, our simulated clusters display a
variety of behaviors in entropy profiles: they range from steadily decreasing
profiles at small radii, characteristic of cool-core systems, to nearly flat
core isentropic profiles, characteristic of non-cool-core systems. Using
observational criteria to distinguish between the two classes of objects, we
find that they occur in similar proportions in both simulations and in
observations. Furthermore, we also find that simulated cool-core clusters have
profiles of iron abundance that are steeper than those of NCC clusters, which
is also in agreement with observational results. We show that the capability of
our simulations to generate a realistic cool-core structure in the cluster
population is due to AGN feedback and artificial thermal diffusion: their
combined action allows us to naturally distribute the energy extracted from
super-massive black holes and to compensate for the radiative losses of
low-entropy gas with short cooling time residing in the cluster core.
