  Two-dimensional systems are realized experimentally as thin layers on a
substrate. The substrate can have some imperfections (defects of the
crystalline structure, chemical impurities, etc.), which demonstrate stronger
interaction with the particles of the two-dimensional layer than the rest of
the system. Such randomly distributed centers of strong interactions are called
"pinning centers". The presence of random pinning can substantially change the
behavior of the system. It not only shifts the melting point of the system, but
can also change the melting scenario itself. In the present paper the influence
of Gaussian pinning on the melting scenario of a two-dimensional system of soft
disks is studied by means of molecular dynamics simulation. We randomly
introduce into the system of soft disks a set of "pinning centers" which
attract the particles via the Gauss potential. We observe that increasing the
depth of a Gaussian well leads to a change in the melting scenario of the
system. The results demonstrate that simple kind of quenched disorder can
significantly affect the melting scenario of two-dimensional systems, offering
the possibility of its introduction in complex experiments and studying its
influence on the self-assembly and phase diagram of two-dimensional systems in
rotating external fields.
