  The random disorder can drastically change the melting scenario of
two-dimensional systems and has to be taken into account in the interpretation
of the experimental results. We present the results of the molecular dynamics
simulations of the two dimensional system with the core-softened potentials
with two repulsive steps in which a small fraction of the particles is pinned,
inducing quenched disorder. It is shown that without the quenched disorder the
system with small repulsive shoulder, which is close in the shape to the soft
disks, melts in accordance with the melting scenario proposed in Refs.
[30,31,33] (first-order liquid-hexatic and continuous hexatic-solid
transitions). Random pinning widens the hexatic phase, but leaves the melting
scenario unchanged. For the system with larger repulsive step at high densities
the conventional first-order transition takes place without random pinning.
However, in the presence of disorder the single first-order transition
transforms into two transitions, one of them (solid-hexatic) is the continuous
KTHNY-like transition, while the hexatic to isotropic liquid transition occurs
as the first order transition.
