The applicability of the one-parameter scaling hypothesis to nonreciprocal high-dimensional disordered systems, specifically, those in dimensions higher than the critical dimension $d_c=2$, as predicted by the standard one-parameter scaling theory of Anderson localization, remains unresolved. In this work, we propose that the size dependence of the reduced participation ratio $Y_L$ in nonreciprocal $d$-dimensional systems of size $L^d$ follows a universal one-parameter scaling form. This feature is encapsulated by the one-parameter $\beta$ function $\beta \left[Y_L\right]=dln\left[Y_L\right]/dln\left[L\right]$, which describes the critical properties of Anderson localization transitions, including the critical exponent $\nu$, the fractal dimension $D$, and the critical reduced participation ratio $Y_L^{*}$. We demonstrate the applicability of our one-parameter scaling theory across the AI, A, and AII classes of three-dimensional nonreciprocal systems under periodic boundary conditions and further extend our analysis to higher dimensions in the presence of nonreciprocity, specifically $d=4$, 5, and 6. Our one-parameter scaling theory also applies to nonreciprocal systems with open boundary conditions, where all states are non-Hermitian skin modes. The scaling analysis indicates that open nonreciprocal systems do not exhibit genuine extended states extending throughout the system in the thermodynamic limit.

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• Anderson localization
• Disordered systems
• Non-Hermitian systems
• Critical exponents
• Finite-size scaling