A novel approach to discontinuous bond percolation transition
Theoretical Condensed Matter Physics Division, Saha Institute of Nuclear Physics - 1/AF Bidhan Nagar, Kolkata, 700064 India
Accepted: 11 April 2011
We introduce a bond percolation procedure on a D-dimensional lattice where two neighbouring sites are connected by N channels, each operated by valves at both ends. Out of a total of N, randomly chosen n valves are open at every site. A bond is said to connect two sites if there is at least one channel between them, which has open valves at both ends. We show analytically that in all spatial dimensions, this system undergoes a discontinuous percolation transition in the N→∞ limit when crosses a threshold. It must be emphasized that, in contrast to the ordinary percolation models, here the transition occurs even in one-dimensional systems, albeit discontinuously. We also show that a special kind of discontinuous percolation occurs only in one dimension when N depends on the system size.
PACS: 64.60.ah – Percolation / 64.60.-i – General studies of phase transitions / 64.60.De – Statistical mechanics of model systems (Ising model, Potts model, field-theory models, Monte Carlo techniques, etc.)
© EPLA, 2011