A physical system consisting of many particles can be described on two levels: Microscopically it is determined by its configuration, i.e., by the positions and momenta of all particles. Knowing a configuration of a system which obeys the laws of classical mechanics and which is not influenced from outside allows one in principle to determine its exact configuration at any future time. Of course, the configuration of a realistic large system cannot even approximately be known. On the other hand, a good description of the macroscopic properties of such a system is provided by a relatively small number of observable parameters like total energy, temperature, entropy, etc. These macroscopic properties are modelled, in mathematics, as parameters associated with probability distributions on the space of all configurations.


Partition Function Critical Temperature Planar Graph Ising Model Satisfying State 
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© Vieweg+Teubner | GWV Fachverlage GmbH 2010

Authors and Affiliations

  • Martin Loebl
    • 1
  1. 1.Department of Applied Mathematics, Institut of Theoretical Computer ScienceCharles UniversityPrahaTschechische Republik

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