Anomalous scaling and Lee-Yang zeros in self-organized criticality

We show that the generating functions of probability distributions in self-organized criticality (SOC) models exhibit a Lee-Yang phenomenon [Phys. Rev. 87, 404 (1952)]. Namely, their zeros pinch the real axis at $z=1,$ as the system size goes to infinity. This establishes a new link between the classical theory of critical phenomena and SOC. A scaling theory of the Lee-Yang zeros is proposed in this setting.