The Liquid--Hexatic Transition for Soft Disks

We study the liquid--hexatic transition of soft disks with massively parallel simulations and determine the equation of state as a function of system size. For systems with interactions decaying as the inverse $m$th power of the separation, the liquid--hexatic phase transition is continuous for $m = 12$ and $m=8$, while it is of first order for $m = 24$. The critical power $m$ for the transition between continuous and first-order behavior is larger than previously reported. The continuous transition for $m=12$ implies that the two-dimensional Lennard-Jones model has a continuous liquid--hexatic transition at high temperatures. We also study the Weeks--Chandler--Andersen model and find a continuous transition at high temperatures, that is consistent with the soft-disk case for $m=12$. Pressure data as well as our implementation are available from an open-source repository.