  We investigate how the dimensionality of the embedding space affects the
microscopic crackling dynamics and the macroscopic response of heterogeneous
materials. Using a fiber bundle model with localized load sharing computer
simulations are performed from 1 to 8 dimensions slowly increasing the external
load up to failure. Analyzing the constitutive curve, fracture strength and
avalanche statistics of bundles we demonstrate that a gradual crossover emerges
from the universality class of localized behavior to the mean field class of
fracture as the embedding dimension increases. The evolution between the two
universality classes is described by an exponential functional form.
Simulations revealed that the average temporal profile of crackling avalanches
evolves with the dimensionality of the system from a strongly asymmetric shape
to a symmetric parabola characteristic for localized stresses and homogeneous
stress fields, respectively.
