We perform extensive simulations of 10(4) Lennard-Jones particles to s
tudy the effect of particle size dispersity on the thermodynamic stabi
lity of two-dimensional solids. We find a novel phase diagram in the d
ispersity-density parameter space. We observe that for large values of
density there is a threshold value of the size dispersity above which
the solid melts to a liquid along a line of first order phase transit
ions. For smaller values of density, our results are consistent with t
he presence of an intermediate hexatic phase. Further, these findings
support the possibility of a multicritical point in the dispersity-den
sity parameter space.