We investigate the full phase diagram of the frustrated J1-J2 Ising model on the two-dimensional honeycomb lattice, incorporating both nearest-neighbor interaction J1 and next-nearest-neighbor interaction J2 using the Wang–Landau Monte Carlo method combined with finite-size scaling analysis. We map out the zero- and finite-temperature phase diagrams as a function of J2/J1. From the entropy profile, we identify four distinct ground-state structures — ferromagnetic, antiferromagnetic, dimer, and stripe states — and confirm that the residual entropy scales linearly with the lattice’s linear dimension in the stripe and dimer ground states. Our results suggest that the transition from the paramagnetic phase into the dimer or stripe phase changes its nature from first-order to continuous while the transition into the ferromagnetic or antiferromagnetic phase is continuous and belongs to the two-dimensional Ising universality class.

Schelling's segregation model demonstrates how simple local rules can generate large-scale social patterns, yet it assumes agents act myopically and ignore the broader consequences of their moves. We extend this framework by introducing social orientation as a behavioral microfoundation, reflecting humans' communal nature. Socially oriented agents follow boundedly rational heuristics that account for the satisfaction of prospective neighbors within a two-step horizon of observability, in addition to their own. We formalize this through three relocation rules-negative externality avoiding (NEA), positive externality favoring (PEF), and positive externality optimizing (PEO)-each capturing a different balance between minimizing disruption and promoting stability. Agent-based simulations reveal that these rules, while maintaining satisfaction, consistently reduce segregation, accelerate the attainment of global stability, and lower relocation moves per agent, thereby reducing social costs. These results provide a stronger behavioral foundation for segregation modeling and show how locally rational, socially sensitive decision-making can scale into equilibria that are not just welfare-enhancing but also yield more integrated and resilient communities.