Influence of quenched disorder on absorbing phase transitions in the conserved lattice gas model

Continuous and discontinuous absorbing-state phase transitions on Voronoi-Delaunay random lattices

We study absorbing-state phase transitions (APTs) in two-dimensional Voronoi-Delaunay (VD) random lattices with quenched coordination disorder. Quenched randomness usually changes the criticality and destroys discontinuous transitions in low-dimensional nonequilibrium systems. We performed extensive simulations of the Ziff-Gulari-Barshad model, and verified that the VD disorder does not change the nature of its discontinuous transition. Our results corroborate recent findings of Barghathi and Vojta [H. Barghathi and T. Vojta, Phys. Rev. Lett. 113, 120602 (2014)PRLTAO0031-900710.1103/PhysRevLett.113.120602], stating the irrelevance of topological disorder in a class of random lattices that includes VD, and raise the interesting possibility that disorder in nonequilibrium APT may, under certain conditions, be irrelevant for the phase coexistence. We also verify that the VD disorder is irrelevant for the critical behavior of models belonging to the directed percolation and Manna universality classes.

Critical properties of the Ziff, Gulari, and Barshad (ZGB) model with inert sites

We study the model proposed by Ziff, Gulari, and Barshad to mimic the oxidation of carbon monoxide (CO) in the presence of fixed impurities distributed over the catalytic surface. Our focus is on the continuous phase transition between the active phase, where occurs the production of carbon dioxide (CO2), and the inactive phase, where all the non inert sites become filled with oxygen molecules. We employ Monte Carlo simulations to calculate the different ratios between moments of the order parameter at the critical point, as well as, we determine the critical exponents β and ν⊥ as a function of the concentration of impurities. We show that the presence of impurities over the catalytic surface changes the critical behavior of the system. The critical exponents depend on the concentration of impurities and the model does not belong to the directed percolation universality class.

Universality class of the conserved Manna model in one dimension

The nonequilibrium absorbing phase transition of the discrete conserved Manna model was studied via Monte Carlo simulations on a one-dimensional chain, using the natural initial states with a sequential update. The critical density of the particles was found to be smaller than the recently reported value, and the order-parameter exponent was considerably different from the directed percolation (DP) value. The influence of quenched disorder was also studied on a diluted strip of L_{x}×L_{y} lattice sites with L_{x}≫L_{y}, and the results were compared with those of the contact process (CP). It was found that the Manna model and the CP exhibited distinctly different behaviors; the CP exhibited nonuniversal power-law decreases of active-site densities in the Griffith phase, whereas the Manna model showed a standard critical behavior. These results consistently suggest that the Manna model belongs to a universality class that is different from the DP class.

Determination of the critical exponents for absorbing phase transitions in the conserved lattice gas model in three dimensions

The critical exponents were measured for absorbing phase transitions in the conserved lattice gas (CLG) model on a simple cubic lattice. The correlation-length exponent calculated from the dynamic exponent obtained by finite-size scaling and from the mean spreading distance was consistently found to be ν(⊥)=0.631±0.02, which yields a positive specific heat exponent α=2-dν(⊥) on a pure system. The pure fixed point should, thus, be unstable if the Harris criterion established in equilibrium systems is applicable to the nonequilibrium absorbing phase transitions of the CLG model. However, this prediction is in contradiction with recent simulation results.