  It is difficult to derive the solid--fluid transition from microscopic
models. We introduce particle systems whose potentials do not decay with
distance and calculate their partition function exactly using a method similar
to that for lattice systems with infinite-range interaction. In particular, we
investigate the behaviors of examples among these models, which become a
triangular, body-centered cubic, face-centered cubic, or simple cubic lattice
in low-temperature phase. The transitions of the first three examples are of
the first order, and that of the last example is of the second order. Note that
we define the solid phase as that whose order parameter, or Fourier component
of the density, becomes nonzero, and the models we considered obey the
ideal-gas law even in the solid phase.
