  Despite about forty years of investigations, the nature of the melting
transition in two dimensions is not completely clear. In the framework of the
most popular Berezinskii-Kosterlitz-Thouless-Halperin-Nelson-Young (BKTHNY)
theory, 2D systems melt through two continuous Berezinskii-Kosterlitz-Thouless
(BKT) transitions with intermediate hexatic phase. The conventional first-order
transition is also possible. On the other hand, recently on the basis of
computer simulations the new melting scenario was proposed with continuous BKT
type solid-hexatic transition and first order hexatic-liquid transition.
However, in the simulations the hexatic phase is extremely narrow that makes
its study difficult. In the present paper, we propose to apply the random
pinning to investigate the hexatic phase in more detail. The results of
molecular dynamics simulations of two dimensional system having core-softened
potentials with narrow repulsive step which is similar to the soft disk system
are outlined. The system has a small fraction of pinned particles giving
quenched disorder. Random pinning widens the hexatic phase without changing the
melting scenario and gives the possibility to study the behavior of the
diffusivity and order parameters in the vicinity of the melting transition and
inside the hexatic phase.
