  In this study we present a Microcanonical Monte Carlo investigation of one
dimensional self-gravitating toy models. We study the effect of hard-core
potentials and compare to those results obtained with softening parameters and
also the effect of the geometry of the models. In order to study the effect of
the geometry and the borders in the system we introduce a model with the
symmetry of motion in a line instead of a circle, which we denominate as $1/r$
model. The hard-core particle potential introduces the effect of the size of
particles and, consequently, the effect of the density of the system that is
redefined in terms of the packing fraction of the system. The latter plays a
role similar to the softening parameter $\epsilon$ in the softened particles'
case. In the case of low packing fractions both models with hard-core particles
show a behavior that keeps the intrinsic properties of the three dimensional
gravitational systems such as negative heat capacity. For higher values of the
packing fraction the ring the system behaves as the Hamiltonian Mean Field
model and while for the $1/r$ it is similar to the one-dimensional systems.
