Open access
Date
2012-04-02Type
- Journal Article
Abstract
Discretized landscapes can be mapped onto ranked surfaces, where every element (site or bond) has a unique rank associated with its corresponding relative height. By sequentially allocating these elements according to their ranks and systematically preventing the occupation of bridges, namely elements that, if occupied, would provide global connectivity, we disclose that bridges hide a new tricritical point at an occupation fraction p = pc, where pc is the percolation threshold of random percolation. For any value of p in the interval pc < p ≤ 1, our results show that the set of bridges has a fractal dimension dBB ≈ 1.22 in two dimensions. In the limit p → 1, a self-similar fracture is revealed as a singly connected line that divides the system in two domains. We then unveil how several seemingly unrelated physical models tumble into the same universality class and also present results for higher dimensions. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000047829Publication status
publishedExternal links
Journal / series
Scientific ReportsVolume
Pages / Article No.
Publisher
LondonSubject
Theoretical physics; Statistical physics, thermodynamics and nonlinear dynamicsOrganisational unit
03733 - Herrmann, Hans Jürgen (emeritus) / Herrmann, Hans Jürgen (emeritus)
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