  Monolayer and two-dimensional (2D) systems exhibit rich phase behavior,
compared with 3D systems, in particular, due to the hexatic phase playing a
central role in melting scenarios. The attraction range is known to affect
critical gas-liquid behavior (liquid-liquid in protein and colloidal systems),
but the effect of attraction on melting in 2D systems remains unstudied
systematically. Here, we reveal how the attraction range affects the phase
diagrams and melting scenarios in a 2D system. Using molecular dynamics
simulations we considered the generalized Lennard-Jones system with a fixed
repulsion branch and different power indices of attraction, from long-range
dipolar to short-range sticky-spheres-like. A drop in the attraction range has
been found to reduce the temperature of the gas-liquid critical point, bringing
it closer to the gas-liquid-solid triple point. At high-temperatures,
attraction does not affect the melting scenario that proceeds through the
cascade of solid-hexatic (Berezinski-Kosterlitz-Thouless) and hexatic-liquid
(first-order) phase transitions. In the case of dipolar attraction, we observed
\emph{two triple points}, inherent in a 2D system: hexatic-liquid-gas and
crystal-hexatic-gas, the temperature of the crystal-hexatic-gas triple point is
\emph{below} the hexatic-liquid-gas triple point. This observation may have
far-reaching consequences for future studies, since phase diagrams determine
possible routes of self-assembly in molecular, protein, and colloidal systems,
whereas the attraction range can be adjusted with complex solvents and external
electric or magnetic fields. The results obtained may be widely used in
condensed matter, chemical physics, materials science, and soft matter.
