Stability limits for the supercooled liquid and superheated crystal of Lennard-Jones particles.

We have studied the limits of stability in the first order liquid-solid phase transition in a Lennard-Jones system by means of the short-time relaxation method and using the bond-orientational order parameter Q6 . These limits are compared with the melting line. We have paid special attention to the supercooled liquid, comparing our results with the point where the free energy cost of forming a nucleating droplet goes to zero. We also indirectly estimate the dimension associated to the critical nucleus at the spinodal, expected to be fractal according to mean field theories of nucleation.