We investigate the interplay between nonreciprocal interactions and chemical-potential imbalance in a two-species nonreciprocal Blume-Capel model. Combining a systematic mean-field bifurcation analysis with large-scale Monte Carlo simulations in two and three dimensions, we map the model's dynamical regimes and transitions. Mean-field theory predicts a rich phase structure—disorder, a time-dependent “swap” (limit-cycle) phase, and static ordered states—separated by Hopf, saddle-node on invariant circle, saddle-node of limit cycles, pitchfork, and saddle-node bifurcations. In two dimensions, Monte Carlo simulations reveal that spiral defects destabilize global swapping and, unless vacancies are strongly favored, destroy long-range order. Crucially, a finite single-ion anisotropy ${\mathrm{\Delta }}_{\alpha }=-{\mathrm{\Delta }}_{\beta }$ promotes vacancy occupation in the $\alpha$ species and suppresses nonreciprocal dynamics, thereby restoring a robust static ordered phase. Finite-size scaling of susceptibility and Binder cumulants places the disorder $\to$ static transition firmly in the two-dimensional Ising universality class. Moreover, within the static ordered phase, we observe a crossover that sharpens into a line of first-order phase transitions; these two regimes are separated by a critical point, which is analogous to the liquid-gas coexistence curve terminating at a critical point. In three dimensions, simulations largely mirror mean-field expectations, though swap $\to$ static ordering occurs indirectly via a disordered regime. Our results demonstrate that vacancy energetics provide a simple, experimentally relevant control knob that stabilizes equilibrium-like order in nonreciprocal systems and that defects can generate novel critical behavior.

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• Classical statistical mechanics
• Nonequilibrium lattice models
• Mean field theory
• Monte Carlo methods