Organized by the Institute of Experimental Physics, University of Bialystok and the Institute of Atomic Energy, Swierk under the auspices of the European Crystallographic Association; Committee of Crystallography, the Polish Academy of Sciences; and the Polish Neutron Scattering Society The School is financially supported in part by the International Union of Crystallography; the European Crystallographic Association; the European Office of Aerospace Research & Development; the Ministry of Science and Information Society Technologies; the Warsaw University of Technology; and the University of Bialystok.
		Correlations functions and Phase Transitions - from finite clusters to an infinite system K.-U. Neumann, Dept. of Physics, Loughborough University, UK Topics A simple magnetic model system is considered and investigated. For a finite system, which can be considered to constitute a cluster of magnetic atoms, the partition function for the magnetic subsystem is calculated explicitly. Thus all macroscopic thermodynamic entities of interest, such as specific heat or magnetisation, can be derived. A determination of microscopic properties, such as the magnetic spin-spin correlations function, requires knowledge of the system on a microscopic scale. This is usually provided by the wavefunction of the system. By starting from a finite cluster of 4 atoms the thermodynamics will be investigated on a macroscopic and a microscopic scale. These model calculations will be compared to measurements on a real system. Thereafter the possibility will be explored of extending the description to larger clusters of spin 1 magnetic moments with an explicit attempt to reach a cluster of infinite extent. The development of characteristics associated with a phase transition as a function of cluster size, will be addressed. The approach to a phase transition in the thermodynamic limit is explored, with the thermodynamic limit being reached for volume V and number of magnet atoms N going to infinity V,N-> ∞ with the constraint that their ratio V/N= const remains constant. While finite clusters do not exhibit a proper phase transition in the thermodynamic sense some of their features already indicate the tendency towards a phase transition with increasing cluster size. This is investigated for some measurable quantities including magnetisation and specific heat.