Criticality in one dimension with inverse square-law potentials

We demonstrate that the scaled order parameter for ferromagnetic Ising and three-state Potts chains with inverse square interactions exhibits a univer sal critical jump, in analogy with the superfluid density in helium films. Renormalization-group arguments are combined with numerical simulations of systems containing up to 10(6) lattice sites to accurately determine the cr itical properties of these models. In strong contrast with earlier work, co mpelling quantitative evidence for the Kosterlitz-Thouless-like character o f the phase transition is provided.