2D Nanocluster Model Divergence: Pairwise LJ vs Many-Body Gupta Bonding

Nanophilosophy asks a concrete question long before it asks an abstract one: at what point does a handful of atoms start behaving like "a material" at all? This 2D simulator builds a genuine hexagonal-lattice gold nanocluster atom by atom and evaluates its cohesion under two physically different models — a pairwise Lennard-Jones potential and the many-body Gupta (second-moment tight-binding) potential used in real nanocluster research — calibrated to agree exactly at full lattice coordination. Grow the cluster, extend the interaction cutoff, and watch edge atoms light up where the two models disagree, while a live radial profile plot shows the divergence shrinking toward the bulk limit as N grows.