  The critical behaviour of a Random Fiber Bundle Model with mixed uniform
distribution of threshold strengths and global load sharing rule is studied
with a special emphasis on the nature of distribution of avalanches for
different parameters of the distribution. The discontinuity in the threshold
strength distribution of fibers non-trivially modifies the critical stress as
well as puts a restriction on the allowed values of parameters for which the
recursive dynamics approach holds good. The discontinuity leads to a
non-universal behaviour in the avalanche size distribution for smaller values
of avalanche size. We observe that apart from the mean field behaviour for
larger avalanches, a new behaviour for smaller avalanche size is observed as a
critical threshold distribution is approached. The phenomenological
understanding of the above result is provided using the exact analytical result
for the avalanche size distribution. Most interestingly,the prominence of
non-universal behaviour in avalanche size distribution depends on the system
parameters.
