Effect of discontinuity in the threshold distribution on the critical behavior of a random fiber bundle

The critical behavior 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 nontrivially 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 nonuniversal behavior in the avalanche size distribution for smaller values of avalanche size. We observe that apart from the mean field behavior for larger avalanches, a new behavior 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 nonuniversal behavior in avalanche size distribution depends on the system parameters.