banner.gif - 12307 Bytes

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.

International Union of CrystallographyEuropean Crystallographic AssociationEuropean Office of Aerospace Research and DevelopmentMinistry of Science and Information Society Technologies  Warsaw University of TechnologyUniversity 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.