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Physics of small systems

Thermodynamical quantities are usually defined in the thermodynamic limit, i.e. for infinite large system size and particle number density. As the system size is decreased, phase transitions become less well defined and eventually a qualitatively different behavior of systems comprising just a very few particle (lets say below 50) should occur. Such small clusters are investigated applying super paramagnetic colloids to two-dimensional cavities with quadratic, hexagonal or circular shapes. At low temperatures and in the case of circular cavities the clusters are found not to crystallize in a triangular lattice (Wigner crystal), but are arranged in a shell structure. Accordingly, it was pointed out that such systems may be a “realization” of a 2D Thomson atom where the structure as a function of the particle number can be analyzed in terms of a Mendeleev-type table.
Thermal fluctuations are well known to have a strong influence on the phase behaviour of two-dimensional (2D) systems compared to their three-dimensional counterparts. The most striking evidence for such a difference is probably the melting transition which is in 2D predicted to ovvur via two sequential defect-driven continuos phase transitions as describes by the KTHNY theory. While KTHNY theory applies only for extended 2D systems, much less is known about the properties of 2D systems which are only comprised of a few particles (typically less than N=100).
Due to the finiteness of such systems a different melting scenario compared to infinite systems is expected which may be important for the understanding of melting and freezing. It has been experimentally demonstrated that when super paramagnetic colloidal particles are confined to a circular hard-wall cavity, the particles at low effective temperatures T.