Jamming is a first-order transition with quenched disorder in amorphous materials sheared by cyclic quasistatic deformations.

Jamming is an athermal transition between flowing and rigid states in amorphous systems such as granular matter, colloidal suspensions, complex fluids and cells. The jamming transition seems to display mixed aspects of a first-order transition, evidenced by a discontinuity in the coordination number, and a second-order transition, indicated by power-law scalings and diverging lengths. Here we demonstrate that jamming is a first-order transition with quenched disorder in cyclically sheared systems with quasistatic deformations, in two and three dimensions. Based on scaling analyses, we show that fluctuations of the jamming density in finite-sized systems have important consequences on the finite-size effects of various quantities, resulting in a square relationship between disconnected and connected susceptibilities, a key signature of the first-order transition with quenched disorder. This study puts the jamming transition into the category of a broad class of transitions in disordered systems where sample-to-sample fluctuations dominate over thermal fluctuations, suggesting that the nature and behavior of the jamming transition might be better understood within the developed theoretical framework of the athermally driven random-field Ising model.