title: From damage percolation to crack nucleation through finite size criticality.
abstract: We present a unified theory of fracture in disordered brittle media that reconciles apparently conflicting results reported in the literature. Our renormalization group based approach 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, we predict a crossover with mean-field avalanche scaling. We discuss intriguing connections to other phenomena where critical scaling is only observed in finite size systems and disappears in the thermodynamic limit.
authors.affiliation: LASSP, Physics Department, Clark Hall, Cornell University, Ithaca, New York 14853-2501, USA.
authors.forename: Ashivni
authors.initials: A
authors.lastname: Shekhawat
authors.forename: Stefano
authors.initials: S
authors.lastname: Zapperi
authors.forename: James P
authors.initials: JP
authors.lastname: Sethna