  The phase transition near 40~$^{\circ }$C of both as-grown thin epitaxial
MnAs films prepared by molecular beam epitaxy on GaAs(001) and nanometer-scale
disks fabricated from the same films is studied. The disks are found to exhibit
a pronounced hysteresis in the temperature curve of the phase composition. In
contrast, supercooling and overheating take place far less in the samples of
continuous layers. These phenomena are explained in terms of the necessary
formation of nuclei of the other phase in each of the disks independent from
each other. The influence of the elastic strains in the disks is reduced
considerably.
