Dresden 2014 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 8: Critical Phenomena and Phase Transitions

DY 8.5: Talk

Monday, March 31, 2014, 16:00–16:15, ZEU 118

Self-avoiding walks and Θ-polymers on crititcal percolation clusters — •Niklas Fricke and Wolfhard Janke — Institut für Theoretische Physik and Centre for Theoretical Sciences (NTZ), Universität Leipzig, Postfach 100920, 04009 Leipzig, Germany

Self-avoiding walks (SAWs) on critical percolation clusters are a basic model for polymers in crowded disordered media. The fractal nature of the clusters gives rise to interesting scaling behavior of the SAWs, which is still poorly understood despite considerable efforts in the past. We developed an exact enumeration method which exploits the fractal structure of the critical cluster [1]. The method can handle walks of several thousand steps, amounting to over 10¹⁰⁰⁰ conformations. This enables us to determine the SAW scaling exponents on critical percolation clusters with unprecedented accuracy. We also look at self-attracting SAWs, a.k.a. Θ-polymers. Here, the comprehensive information obtained via exact enumeration is particularly valuable as it allows for a close analysis of temperature-driven phase transitions.

[1] N. Fricke and W. Janke, Europhys. Lett. 99, 56005 (2012).