Towards a Unifying Scaling Theory of Rigidity Transitions

A large class of models describing various athermal disordered systems such as granular materials, living tissues, and polymer networks exhibit transitions from fluid or floppy states to rigid states. In some cases, the transition marks the boundary between the underconstrained region of parameter space to the overconstrained region, while in other cases, the transition takes place entirely in the underconstrained region as strain is varied. We study a spring-network model that exhibits both types of transitions and provide a unifying perspective based on a scaling ansatz for the rigidity transition in this model.