First Order Rigidity Transition in Random Rod Networks

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Abstract
We study the transition from the flexible to the rigid state in a system of randomly placed rigid rods connected by free joints. At the percolation transition point the system is still flexible and the transition to the macroscopically rigid state occurs at a higher concentration of bonds. It is shown that, in contrast to the percolation transition, the rigidity transition is analogous to the first order transition in thermodynamical systems: the rigidity correlation length is finite at the transition point, there is a finite jump in the magnitude of the order parameter, there are similarities with the new phase nucleation processes, etc.