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Monolayer and two-dimensional (2D) systems exhibit rich phase behavior,compared with 3D systems, in particular, due to the hexatic phase playing acentral role in melting scenarios. The attraction range is known to affectcritical gas-liquid behavior (liquid-liquid in protein and colloidal systems),but the effect of attraction on melting in 2D systems remains unstudiedsystematically. Here, we reveal how the attraction range affects the phasediagrams and melting scenarios in a 2D system. Using molecular dynamicssimulations we considered the generalized Lennard-Jones system with a fixedrepulsion branch and different power indices of attraction, from long-rangedipolar to short-range sticky-spheres-like. A drop in the attraction range hasbeen found to reduce the temperature of the gas-liquid critical point, bringingit closer to the gas-liquid-solid triple point. At high-temperatures,attraction does not affect the melting scenario that proceeds through thecascade 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 andcrystal-hexatic-gas, the temperature of the crystal-hexatic-gas triple point is\emph{below} the hexatic-liquid-gas triple point. This observation may havefar-reaching consequences for future studies, since phase diagrams determinepossible routes of self-assembly in molecular, protein, and colloidal systems,whereas the attraction range can be adjusted with complex solvents and externalelectric or magnetic fields. The results obtained may be widely used incondensed matter, chemical physics, materials science, and soft matter.

The role of attraction in the phase diagrams and melting scenarios of generalized 2D Lennard-Jones systems