  Heat capacity curves as functions of temperature for classical atomic
clusters bound by pairwise Lennard-Jones potentials were calculated for
aggregate sizes from 4 to 24 using Monte Carlo methods. J-walking (or
jump-walking) was used to overcome convergence difficulties due to
quasi-ergodicity in the solid-liquid transition region. The heat capacity
curves were found to differ markedly and nonmonotonically as functions of
cluster size. Curves for N = 4, 5 and 8 consisted of a smooth, featureless,
monotonic increase throughout the transition region, while curves for N = 7 and
15-17 showed a distinct shoulder in this region; the remaining clusters had
distinguishable transition heat capacity peaks. The size and location of these
peaks exhibited "magic number" behavior, with the most pronounced peaks
occurring for magic number sizes of N = 13, 19 and 23. A comparison of the heat
capacities with other cluster properties in the solid-liquid transition region
that have been reported in the literature indicates partial support for the
view that, for some clusters, the solid-liquid transition region is a
coexistence region demarcated by relatively sharp, but separate, melting and
freezing temperatures; some discrepancies, however, remain unresolved.
