Absorbing phase transitions in diluted conserved threshold transfer process

Abstract

Absorbing phase transitions in the conserved threshold transfer process (CTTP) on diluted lattices, i.e., on infinite percolation networks, were studied in two dimensions by Monte Carlo simulations. Lattice dilution was found to be irrelevant to the critical behavior for the concentration of diluted sites $x$ far less than the critical concentration ${x}_{c}$ ($=1\ensuremath{-}{p}_{c}$, with ${p}_{c}$ being the percolation threshold), whereas for $x$ close to ${x}_{c}$ the critical exponents slightly deviated from those of the pure CTTP and new critical exponents were established at ${x}_{c}$. The results for $x<{x}_{c}$ were consistent with the recent results for the conserved lattice gas (CLG) model, whereas the results for $x={x}_{c}$ were different from those of the CLG model, for which nonuniversal power-law behavior was observed [Lee, Phys. Rev. E 84, 041123 (2011)]. On the other hand, the critical exponents of the CTTP on a percolation backbone were similar to those on an infinite network and similar to those of the CLG model on a backbone network. The diluted CTTP in three and four dimensions was also investigated, and the critical exponents were similar to those in two dimensions; i.e., the critical exponents were independent of or weakly dependent on the dimensionality. A comment on the recent claim of the absence of a Manna class was also presented.