Berlin 2018 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 10: Statistical Physics I (General)

DY 10.1: Talk

Monday, March 12, 2018, 10:00–10:15, BH-N 333

Scaling behavior of self-avoiding walks on critical percolation clusters in two to seven dimensions from exact enumeration — •Wolfhard Janke and Niklas Fricke — Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, 04009 Leipzig, Germany

We study the scaling behavior of self-avoiding walks on critical percolation clusters by means of a recently developed exact enumeration method, which can handle walks of several thousand steps. We had previously presented results for the two- and three-dimensional cases; here we take a wider perspective and vary the system’s dimensions up to D=7, beyond the supposed upper critical dimension of D_uc=6. These results may serve as a check of analytical predictions and help understand how the medium’s fractal structure impacts on the walks’ scaling behavior. For the physically relevant, smaller dimensions, the scaling exponent ν for the end-to-end distance turns out to be smaller than previously thought and appears to be the same on the backbones as on full clusters. For the number of conformations, the “partition function”, we find strong evidence against the widely assumed scaling law and propose an alternative, which perfectly fits our data.

[1] N. Fricke and W. Janke, Phys. Rev. Lett. 113, 255701 (2014).

[2] N. Fricke and W. Janke, J. Phys. A 50, 264002 (2017).