Berlin 2005 – wissenschaftliches Programm
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DY: Dynamik und Statistische Physik
DY 50: Critical Phenomena and Phase Transitions
DY 50.8: Vortrag
Mittwoch, 9. März 2005, 11:45–12:00, TU H3010
Calculation of partition functions by measuring distributions of number of components — •Alexander K. Hartmann — Institut für Theoretische Physik, Friedrich-Hund-Platz 1, 37077 Göttingen
A new algorithm is presented, which allows to calculate numerically the partition function Z for systems, which can be described by arbitrary interaction graphs and lattices, e.g. Ising models or Potts models (for arbitrary values q>0), including random or diluted models. The new approach is suitable for large systems. The basic idea is to measure the distribution of the number of connected components in the corresponding Fortuin-Kasteleyn representation and to compare with the case of zero degrees of freedom, where the exact result Z=1 is known. As application, d=2 and d=3-dimensional ferromagnetic Potts models are studied, and the critical values qc, where the transition changes from second to first order, are determined. Large systems of sizes N=10002 respectively N=1003 are treated. The critical value qc(d=2)=4 is confirmed and qc(d=3)=2.35(5) is found.