Berlin 2005 – wissenschaftliches Programm
Bereiche | Tage | Auswahl | Suche | Downloads | Hilfe
DY: Dynamik und Statistische Physik
DY 34: Poster
DY 34.110: Poster
Montag, 7. März 2005, 15:30–18:00, Poster TU D
Series expansions for disordered Potts models — •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. This method enables the exact calculation of quenched disorder averages for arbitrary uncorrelated coupling distributions. Moreover, we can keep the disorder strength p as well as the dimension d as symbolic parameters. By applying several series analysis techniques to the new series expansions, one can scan large regions of the (p,d) parameter space for any value of q. We present results for the transition temperature and the effective critical exponent γ as a function of p for the diluted Ising model in three dimensions and discuss the observed crossover behaviour. As a by-product we get high-temperature series in the parameter q for pure q-state Potts models up to order 19 which allow us to analyze the different q→0 limits (percolation, tree percolation) in various dimensions.