Abstract
Using a recently developed algorithm for generic rigidity of two-dimensional graphs, we analyze rigidity and connectivity percolation transitions in two dimensions on lattices of linear size up to We compare three different universality classes: the generic rigidity class, the connectivity class, and the generic “braced square net”(GBSN). We analyze the spanning cluster density the backbone density , and the density of dangling ends In the generic rigidity (GR) and connectivity cases, the load-carrying component of the spanning cluster, the backbone, is fractal at so that the backbone density behaves as for We estimate for generic rigidity and for the connectivity case. We find the correlation length exponents for generic rigidity compared to the exact value for connectivity, In contrast the GBSN undergoes a first-order rigidity transition, with the backbone density being extensive at and undergoing a jump discontinuity on reducing p across the transition. We define a model which tunes continuously between the GBSN and GR classes, and show that the GR class is typical.
- Received 22 September 1998
DOI:https://doi.org/10.1103/PhysRevE.59.2614
©1999 American Physical Society