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 − 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.

Monte Carlo simulations of polymers with nearest- and next nearest-neighbor interactions on square and cubic lattices

“…In similar plots for = K K , respectively. The last value is in good agreement with several previous estimates (see table 1 from [8]), while the other values are slightly larger than the ones reported in [21], where the last value is also underestimated, which is possible due to the small polymer lengths considered there ( ⩽ N 38). It is interesting to notice that, considering energies and k B equal unity, the results above leads to…”

“…Namely, critical exponents ν t , ϕ t and γ t in good agreement with the Θ ones were found along the (transition) Θ-line, in both square and cubic lattices. In the first one, the Θ-line seems to have a linear behavior in the phase diagram, as already observed for this model [21]. Along the Θ-lines, the growth parameters, from the partition function, have monotonic behaviors decreasing (increasing) with K 1 (K 2 ).…”

“…, which is slightly above our line (see figure 3). Hence, the critical temperatures there are smaller than the ones here, possible due to the small lengths handled in [21]. , respectively.…”

“…More recently, another generalization of the ISAW model was proposed by Lee et al [20,21], which considered attractive interactions, with energies ϵ 1 and ϵ 2 , between NN and next-nearest-neighbor (NNN) monomers, respectively. They calculate exactly the partition function zeros for chains with up to 38 monomers on the square lattice and showed that the crossover exponent is not affected by the NNN interaction.…”

“…Phase diagram of the generalized ISAW model on the square lattice. The full (red) line is given by equation (8), while the dashed (blue) line is the result from[21].…”