Dresden 2006 – wissenschaftliches Programm

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DY: Dynamik und Statistische Physik

DY 46: Poster

DY 46.119: Poster

Donnerstag, 30. März 2006, 16:00–18:00, P1

Series expansions for percolation and bond-diluted Ising models on Z^D — •Meik Hellmund¹ and Wolfhard Janke² — ¹Mathematisches Institut, Universität Leipzig — ²Institut für Theoretische Physik, Universität Leipzig

We derive high-temperature series expansions for the free energy and the susceptibility of random-bond q-state Potts models on hypercubic lattices using a star-graph expansion technique.

For the case of the Ising (q=2) model, disordered by quenched bond dilution, a detailed analysis of the influence of the disorder on the second-order phase transition (change in critical temperature and exponent γ) is presented for 3, 4 and 5 dimensions.

In the pure (no disorder) case we obtain series for the free energy and susceptibility with explicit q- and D-dependence up to order 17 (arbitrary D) and 19 (D≤5), resp. This allows us to analyze bond percolation (q→1) and tree percolation (q→0) and obtain critical exponents in various dimensions.