Crossover Scaling of Binder Cumulant and its application in Non-reciprocal Sandpiles

Abstract

In this letter, we unveil a robust, pre-asymptotic scaling regime for the Binder cumulant $U_L$, a central finite-size scaling tool, demonstrating $U_L\sim N^{-1} |t|^{-d\nu}$ (disordered phase) and $\frac{2}{3}-U_L\sim N^{-1} |t|^{-d\nu}$ (ordered phase), with $t$ being the reduced control parameter, and $N$, $d$, $\nu$ represent the total number of sites, the dimensionality, and correlation length exponent, respectively. Leveraging this result, we resolve a fundamental question on the stability of universality classes under the breaking of microscopic reciprocity. For the conserved Manna sandpile, we show that reciprocal biases preserve its universality class, merely shifting the critical point. In striking contrast, any non-reciprocal interaction acts as a relevant perturbation, decisively driving the system's critical exponents to flow from their non-mean-field values towards the mean-field related ones. This flow establishes non-reciprocity as a generic mechanism inducing mean-field criticality in conserved, non-equilibrium systems.