Phosphorene monolayers exhibit a range of advanced functional properties; however, their spin configurations and structural phase transitions remain unexplored in the context of enhancing performance in quantum computation and information. In this study, we employ a two-dimensional (2D) Ising model with nearest- and next-nearest-neighbor interactions, denoted as \(J\) and \(J^{\prime }\) respectively, alongside a Monte Carlo approach, to investigate the structural phase transitions and spin behavior of phosphorene. Using this model, we derive the temperature-dependent phase diagram of the phosphorene in terms of the interaction strength ratio ( \(J/J^{\prime }\) ), revealing three distinct phases—checkerboard-ordered, glassy, and quasi-ordered—with a phase boundary at \(J/J^{\prime } = 2\) . Additionally, we analyze the effects of possible defects and strains in the phosphorene lattice induced by the substrate on the phase transitions. Our findings have potential applications in adiabatically switching states through gradual variations in coupling constants, offering new possibilities for adiabatic quantum computing (AQC) and π-ring arrays.
