Regensburg 2004 – wissenschaftliches Programm

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DY: Dynamik und Statistische Physik

DY 46: Poster

DY 46.90: Poster

Donnerstag, 11. März 2004, 16:00–18:00, Poster D

Damage Spreading in Ising Lattice — •Rodrigo Megaides and Wolfhard Janke — Institut für Theoretische Physik, Universität Leipzig, Augustusplatz 10/11, 04109 Leipzig, Germany

We study the “damage spreading phenomenon” in a two-dimensional Ising lattice of different sizes. The phenomenon consists in the propagation of a small modification, in the initial state of the lattice, to the whole system without changing the random noise. The method is first equilibrating the system and then performing a time average over final “Hamming distances" (a measure of the number of spins in opposition in two similar systems) of initial pairs of lattices (the first one taken for such average and the second one being identical to the former except for the individual state of several spins, the so called “damage"). In every individual measurement, we find one of these three types of “final" Hamming distances (HD) : HD = 0 or healing (the damage disappears at the first sweeps), HD ≃ 0.5 or 0.5-spreading (the damage spreads until it reaches one half of the lattices, except for some fluctuations), HD = 1 or infinite spreading (the damage fills the lattice). The probabilities of such cases are obtained (for different temperatures and lattice sizes) from the time average, as well as a mean value of the Hamming distance which is easily calculated from the mentioned probabilities. Some scaling properties are proposed.