Melting and freezing of a skyrmion lattice.

We report comprehensive Monte-Carlo studies of the melting of skyrmion lattices (SkL) in systems of small, medium, and large sizes with the number of skyrmions ranging from 10to over 10. Large systems exhibit hysteresis similar to that observed in real experiments on the melting of SkLs. For sufficiently small systems which achieve thermal equilibrium, a fully reversible sharp solid-liquid transition on temperature with no intermediate hexatic phase is observed.