title: Fracture and second-order phase transitions.
abstract: Using the global fiber bundle model as a tractable scheme of progressive fracture in heterogeneous materials, we define the branching ratio in avalanches as a suitable order parameter to clarify the order of the phase transition occurring at the collapse of the system. The model is analyzed using a probabilistic approach suited to smooth fluctuations. The branching ratio shows a behavior analogous to the magnetization in known magnetic systems with second-order phase transitions. We obtain a universal critical exponent beta approximately = 0.5 independent of the probability distribution used to assign the strengths of individual fibers.
authors.affiliation: Departamento de Fisica Teorica, Universidad de Zaragoza, 50009 Zaragoza, Spain.
authors.forename: Y
authors.initials: Y
authors.lastname: Moreno
authors.forename: J B
authors.initials: JB
authors.lastname: Gomez
authors.forename: A F
authors.initials: AF
authors.lastname: Pacheco