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We study universality classes and crossover behaviors in non-Abelian directedsandpile models, in terms of the metastable pattern analysis. The non-Abelianproperty induces spatially correlated metastable patterns, characterized by thealgebraic decay of the grain density along the propagation direction of anavalanche. Crossover scaling behaviors are observed in the grain density due tothe interplay between the toppling randomness and the parity of the thresholdvalue. In the presence of such crossovers, we show that the broadness of thegrain distribution plays a crucial role in resolving the ambiguity of theuniversality class. Finally, we claim that the metastable pattern analysis isimportant as much as the conventional analysis of avalanche dynamics.

Universality classes and crossover behaviors in non-Abelian directed sandpiles