Phase diagram for brittle fracture in the disorder-system size plane

The authors present a unified theory of fracture in disordered brittle media using a renormalization group based approach, which yields a phase diagram in which the percolation fixed point, expected for infinite disorder, is unstable for finite disorder and flows to a zero-disorder nucleation-type fixed point, thus showing that fracture has a mixed first order and continuous character. In a region of intermediate disorder and finite system sizes, they predict a crossover with mean-field avalanche scaling.

References: 
[1] A. Shekhawat, S. Zapperi, and J. P. Sethna, Phys. Rev. Lett. 110, 185505 (2013)
[2] E. Bouchard, The Breaking of Brittle Materials, Physics 6, 50 (2013)
[3] A. A. Moreira, C. L. N. Oliveira, A. Hansen, N. A. M. Araújo, H. J. Herrmann, and J. S. Andrade Jr., Phys. Rev. Lett. 110, 185505 (2013)