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DY: Fachverband Dynamik und Statistische Physik

DY 7: Critical Phenomena and Phase Transitions

DY 7.5: Talk

Monday, March 18, 2024, 12:45–13:00, BH-N 128

Universal Approach to Critical Percolation — •Fabian Coupette and Tanja Schilling — Institute of Physics, University of Freiburg, Freiburg, Germany

Percolation is an archetypal critical phenomenon that occurs across a diverse range of contexts, such as the design of composite materials or vaccination strategies on community networks. In contrast to the critical exponents, the critical parameters (percolation threshold) characterizing the emergence of a system-spanning connected cluster, depend sensitively on the system properties. As a consequence, theoretical approaches predicting percolation thresholds are rare, often heuristic in nature, and tailored to specific applications.

We propose a general mapping of any kind of percolation problem onto a branching process which provides rigorous lower bounds for the percolation threshold. These bounds progressively tighten as we incorporate more local information into the description. We demonstrate our approach for different lattice and continuum problems obtaining accurate predictions with minimal effort. Our method is based on first principles, reproduces all exact solutions to percolation problems, and does not require fitting parameters. As such it offers an important theoretical reference in a field that is dominated by simulation studies and heuristic descriptions.

Keywords: Percolation; Connectivity; Complex Networks; Critical Phenomena; Stochastic Processes