  Fibrous networks such as collagen are common in physiological systems. One
important function of these networks is to provide mechanical stability for
cells and tissues. At physiological levels of connectivity, such networks would
be mechanically unstable with only central-force interactions. While networks
can be stabilized by bending interactions, it has also been shown that they
exhibit a critical transition from floppy to rigid as a function of applied
strain. Beyond a certain strain threshold, it is predicted that
underconstrained networks with only central-force interactions exhibit a
discontinuity in the shear modulus. We study the finite-size scaling behavior
of this transition and identify both the mechanical discontinuity and critical
exponents in the thermodynamic limit. We find both non-mean-field behavior and
evidence for a hyperscaling relation for the critical exponents, for which the
network stiffness is analogous to the heat capacity for thermal phase
transitions. Further evidence for this is also found in the self-averaging
properties of fiber networks.
