THE ANISOTROPIC BAK-SNEPPEN MODEL

The Bak-Sneppen model is shown to fall into a different universality c lass with the introduction of a preferred direction, mirroring the sit uation in spin systems. This is first demonstrated by numerical simula tions and subsequently confirmed by analysis of the multitrait version of the model, which admits exact solutions in the extremes of zero an d maximal anisotropy. For intermediate anisotropies, we show that the spatiotemporal evolution of the avalanche has a power law 'tail' which passes through the system for any non-zero anisotropy but remains fix ed for the isotropic case, thus explaining the crossover in behaviour. Finally, we identify the maximally anisotropic model which is more tr actable and yet more generally applicable than the isotropic system.