The paper investigates the jamming transition in two- and three-dimensional systems of particles interacting with finite-range, repulsive potentials at zero temperature and zero applied stress. The authors study how these systems develop a yield stress in a disordered state, known as jamming, at a critical packing fraction, $\phi_c$. They find that the distribution of $\phi_c$ values becomes narrower as the system size increases, indicating that essentially all configurations jam at the same packing fraction in the thermodynamic limit. This packing fraction corresponds to the previously measured value for random close-packing. The jamming threshold, Point J, exhibits properties similar to an ordinary critical point, with power-law scaling for quantities like the pressure, shear modulus, and coordination number as they approach $\phi_c$. However, Point J differs from a typical critical point in that the scaling exponents depend on the inter-particle potential rather than the dimensionality. Near Point J, certain quantities no longer self-average, suggesting the existence of a diverging length scale. Additionally, the density of vibrational states develops a large excess of low-frequency modes, and at Point J, the density of states is a constant down to zero frequency. These findings suggest that Point J may control behavior in its vicinity, possibly even at the glass transition.The paper investigates the jamming transition in two- and three-dimensional systems of particles interacting with finite-range, repulsive potentials at zero temperature and zero applied stress. The authors study how these systems develop a yield stress in a disordered state, known as jamming, at a critical packing fraction, $\phi_c$. They find that the distribution of $\phi_c$ values becomes narrower as the system size increases, indicating that essentially all configurations jam at the same packing fraction in the thermodynamic limit. This packing fraction corresponds to the previously measured value for random close-packing. The jamming threshold, Point J, exhibits properties similar to an ordinary critical point, with power-law scaling for quantities like the pressure, shear modulus, and coordination number as they approach $\phi_c$. However, Point J differs from a typical critical point in that the scaling exponents depend on the inter-particle potential rather than the dimensionality. Near Point J, certain quantities no longer self-average, suggesting the existence of a diverging length scale. Additionally, the density of vibrational states develops a large excess of low-frequency modes, and at Point J, the density of states is a constant down to zero frequency. These findings suggest that Point J may control behavior in its vicinity, possibly even at the glass transition.