Two-dimensional fluids under triangle-well-like interactions: A tunable phase behavior

We carried out a detailed molecular dynamics study to investigate the phase behavior of two-dimensional fluids where particles interact through triangular-like pair potentials. Focusing on three representative interaction models-the triangular well (TW), the Jagla-like (JL), and the inverse triangular well (ITW)-we explored how subtle changes in the potential shape influence structural organization and phase transitions. Each model exhibits distinctive behavior. The TW potential reproduces classical 2D phase features, including a well-defined vapor-liquid coexistence and the formation of compact triangular solids. The JL potential, characterized by a soft repulsive ramp, introduces structural frustration that stabilizes low-density square lattices and gives rise to rich polymorphism, including solid-solid coexistence. In contrast, the ITW potential, where attractive and repulsive features overlap, displays the most complex structural diversity, with emergent phases such as dodecagonal and honeycomb-like solids. By analyzing thermodynamic properties, radial distribution functions, and bond-orientational order parameters, we mapped out vapor-liquid, liquid-solid, and solid-solid transitions, revealing how the shape of the interaction potential plays a critical role in governing order, polymorphism, and phase stability in two-dimensional systems. Finally, we confirm the presence of the hexatic phase in systems governed by the TW potential by analyzing both bond-orientational and translational correlation functions. These findings not only support the existence of this intermediate phase but also provide a clear framework for its identification. More broadly, this work lays the groundwork for exploring the hexatic phase across a wide range of discrete pair interaction models in two-dimensional systems, offering new opportunities to understand the subtle mechanisms behind two-step melting and structural transitions.