Bulletin of the American Physical Society
APS March Meeting 2018
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session L60: Poster Session II
Wednesday, March 7, 2018
LACC Room: West Hall A
Abstract: L60.00218 : Exact enumeration of self-avoiding walks on critical percolation clusters in two to seven dimensions*
We study 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 \nu 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.
*Deutsche Forschungsgemeinschaft (DFG): SFB/TRR 102 (Project B04) and JA 483/29-1.
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