We study a two-dimensional fluid of particles interacting through a spherically symmetric and
marginally soft two-body repulsion. This model can exist in three different crystal phases,
one of them with square symmetry and the other two triangular. We show that, while the
triangular solids first melt into a hexatic fluid, the square solid is directly transformed on
heating into an isotropic fluid through a first-order transition, with no intermediate tetratic
phase. In the low-pressure triangular and square crystals, melting is reentrant provided the …