Avalanche-Burst Invasion Percolation: Emergent Scale Invariance on Pseudo-Critical System

As the variety of systems displaying scale invariant characteristics are matched only by their number, it is becoming increasingly important to understand their fundamental and universal elements. Much work has attempted to apply 2nd order phase transition mechanics due to the emergent scale invariance at the critical point. However for many systems, notions of phases and critical points are both artifical and cumbersome. We characterize the critical features of the avalanche burst invasion percolation(AIP) model since it exists as hybrid critical system(of which many self-organized critical systems may fall under). We find behavior strongly representative of critical systems, namely, from the presence of a critical Fisher type distribution, $n_s(\tau, \sigma)$, but other essential features absent like an order parameter and to a lesser degree hyperscaling. This suggests that we do not need a full phase transition description in order to observe scale invariant behavior, and provides a pathway for more suitable descriptions