Universal Scaling of the Chaos Front in 2+1 dimensions

We study the spreading of an initially localized perturbation in a spatially extended system – a many-body analogue of the butterfly effect. The boundary of the spatially spreading perturbation is identified as a chaos front and studied within the framework of interface growth. We study this phenomenon in a reversible momentum-conserving parity-check cellular automaton (MCPCA) on a hexagonal lattice. We consider two initial-state ensembles: a maximal-entropy state and a positive-parity state. In both cases, the perturbation is introduced along a straight line, corresponding to flat initial geometry. The front exhibits ballistic propagation and universal scaling of its fluctuations, with the associated critical exponents consistent with the predictions of the Kardar–Parisi–Zhang (KPZ) universality class. Furthermore, the standardized third and fourth cumulants agree with the Tracy–Widom distribution for the Gaussian orthogonal ensemble (GOE) in flat geometry, providing further evidence for KPZ universality in (1+1) dimensions. We systematically account for finite-time and finite-size effects and compare their scaling with theoretical expectations and results from previous studies.