  A cascade of phase transitions from square to hexagonal lattice is studied in
2D system of particles interacting via core-softened potential. Due to the
presence of two length-scales of repulsion, different local configurations with
four, five, and six neighbors enable, leading to formation of complex crystals.
The previously proposed interpolation method is generalized for calculation of
pair correlations in crystals which elemental cell consists of more than one
particle. A high efficiency of the method is illustrated using a snub square
lattice as a representative example. Using molecular dynamics simulations, it
is found that the snub square lattice is being broken under heating, generating
high density quasicrystalline phase with 12-fold symmetry. Simple theoretical
model is proposed to explain the physical mechanism governing this phenomenon:
With density growth (from square to hexagonal phases), the concentrations of
different local configurations randomly realized through plane tilling are
being changed that minimizes the energy of the system. The calculated phase
diagram in the intermediate region of densities justifies the existence of HD12
phase and demonstrates a cascade of the first-order transitions "square -- HD12
-- hexagonal" solid phases with the density growth. The results allow us to
better understand the physical mechanisms responsive for formation of
quasicrystals, and, therefore, should be of interest for broad community on
material science and soft matter.
