Continuum contact process and influence of impurity on the critical behavior in absorbing-state phase transitions in two dimensions.

We study via Monte Carlo simulations the influence of quenched and mobile impurities in the contact process (CP) on two-dimensional lattice and continuum systems. In the lattice system, the effect of mobile impurity was studied for the density n_{i}=0.2 and two selected values of hopping probability for impurity particles, w=0.5 and 1. In the continuum system, the CP was defined by distributing spherical impurity particles of diameter σ_{i} and number density n_{i}=0.2 and active particles of diameter unity and number density 1-n_{i} on a square substrate with periodic boundaries. In each dynamic process, a particle is selected at random; the active particle either creates with a rate λ an offspring at a distance r (1≤r≤1.5) from the active particle or annihilates with a unit rate, and the impurity particle hops a distance r (0≤r≤1), both along randomly selected directions. We found that the lattice CP shows power-law behaviors with varying critical exponents depending on the values of w. For the continuum CP with quenched impurity, the critical behavior followed the activated scaling scenario, whereas with mobile impurity usual power-law behaviors were observed but the critical exponents varied depending on the values of σ_{i}.

Alternative method for measuring characteristic lengths in absorbing phase transitions.

We applied an alternative method for measuring characteristic lengths reported recently by one of us [J. M. Kim, J. Stat. Mech. (2021) 03321310.1088/1742-5468/abe599] to the models in the Manna universality class, i.e., the stochastic Manna sandpile and conserved lattice gas models in various dimensions. The universality of the Manna model has been under long debate particularly in one dimension since the work of M. Basu et al. [Phys. Rev. Lett. 109, 015702 (2012)10.1103/PhysRevLett.109.015702], who claimed that the Manna model belongs to the directed percolation (DP) universality class and that the independent Manna universality class does not exist. We carried out Monte Carlo simulations for the stochastic Manna sandpile model in one, two, and three dimensions and the conserved lattice gas model in three dimensions, using both the natural initial states (NISs) and uniform initial states (UISs). In two and three dimensions, the results for R(t), defined by R(t)=L[〈ρ_{a}^{2}〉/〈ρ_{a}〉^{2}-1]^{1/d}, L and ρ_{a} being, respectively, the system size and activity density, yielded consistent results for the two initial states. R(t) is proportional to the correlation length following R(t)∼t^{1/z} at the critical point. In one dimension, the data of R(t) for the Manna model using NISs yielded anomalous behavior, suggesting that NISs require much longer prerun time steps to homogenize the distribution of particles and larger systems to eliminate the finite-size effect than those employed in the literature. On the other hand, data from UISs yielded a power-law behavior, and the estimated critical exponents differed from the values in the DP class.

Classification of universality classes for quasideterministic sandpile models.

The critical behavior of the two-state rotational sandpile model proposed by Santra et al. [Phys. Rev. E 75, 041122 (2007)PLEEE81539-375510.1103/PhysRevE.75.041122] and the locally deterministic and globally stochastic three-state sandpile model are investigated via Monte Carlo simulations. Through these simulations, we are able to estimate critical exponents that characterize the avalanche properties, i.e., the probability distributions of the avalanche size, area, lifetime, and gyration radius, and the expectation values of the avalanche size and area against time and of the size against area. The results are compared with those of the known universality classes. The two models are found to yield consistent results within the range of statistical error, and appear to be consistent with the stochastic two-state Manna sandpile model; therefore, both models appear to belong to the Manna universality class. Our results contradict the earlier conclusion of Santra et al., which we attribute to the slow convergence of the probability distribution to the asymptotic power-law behavior, particularly for the size and lifetime of avalanches.

Surface growth on percolation networks by a conserved-noise restricted solid-on-solid growth model.

Surface growth by the conserved-noise restricted solid-on-solid model is investigated on diluted lattices, i.e., on percolation networks that are embedded in two spatial dimensions. The growth exponent ß and the roughness exponent α are defined, respectively, by the mean-square surface width via W(2)(t)∼t(2ß) and the mean-square saturated width via W(sat)(2)(L)∼L(2α), where L is the system size. These are measured on both an infinite network and a backbone network and the results are compared with power-counting predictions obtained using the fractional Langevin equation. While the Monte Carlo results on deterministic fractal substrates show excellent agreement with the predictions [D. H. Kim and J. M. Kim, Phys. Rev. E 84, 011105 (2011)], the results on critical percolation networks deviate by 8%-12% from these predictions.

Absorbing phase transition in a conserved lattice gas model with next-nearest-neighbor hopping in one dimension.

The absorbing phase transition of the modified conserved lattice gas (m-CLG) model was investigated in one dimension. The m-CLG model was modified from the conserved lattice gas (CLG) model in such a way that each active particle hops to one of the nearest-neighbor and next-nearest-neighbor empty sites. The order parameter exponent, the dynamic exponent, and the correlation length exponent were estimated from the power-law behavior and finite-size scaling of the active particle densities. The exponents were found to differ considerably from those of the ordinary CLG model and were also distinct from those of the Manna model, suggesting that next-nearest-neighbor hopping is a relevant factor that alters the critical behavior in the one-dimensional CLG model.

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.

Critical behavior of absorbing phase transitions for models in the Manna class with natural initial states.

The critical behavior of absorbing phase transitions for two typical models in the Manna universality class, the conserved Manna model and the conserved lattice gas model, both on a square lattice, was investigated using the natural initial states. Various critical exponents were estimated using the static and dynamic simulations. The exponents characterizing dynamics of active particles differ considerably from the known exponents obtained using the random initial states, whereas those associated with the steady-state quantities remain the same. The critical exponents for both models were consistent with errors of less than 1% and satisfied the known scaling relations; thus, the known violation of scaling relations for models with a conserved field was resolved using the natural initial states. The results differed by 7%∼12% from the directed percolation values.

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

Motivated by the Harris criterion, the absorbing phase transitions of the conserved lattice gas (CLG) model were studied on lattices with a quenched disorder, i.e., on infinite percolation networks, in two and three dimensions. The Harris criterion suggests that, in a magnetic system, the pure fixed point will be unstable if the specific-heat exponent is positive. For the CLG model, the specific-heat exponent α calculated by the hyperscaling relation α=2-dν, where ν is the spatial correlation length exponent in d dimensions, will be positive in two dimensions if the value of ν obtained earlier by Lübeck and Heger is employed. On the other hand, it will be close to 0 if the more recent value by Lee and Lee is used and it is positive in three dimensions with the available value of ν. Extensive numerical simulations showed that, when the concentration of disordered sites is less than the critical concentration, the critical exponents were similar to those on a regular lattice both in two and three dimensions. When the concentration of disordered sites becomes critical, the density of active particles showed nonuniversal power-law behavior for all particle densities considered in both dimensions. These results were in contrast to the results for the diluted contact process. The cause of such a nonuniversal behavior was addressed.

Scaling in film growth by pulsed laser deposition and modulated beam deposition.

The scalings in film growth by pulsed laser deposition (PLD) and modulated beam deposition (MBD) were investigated by Monte Carlo simulations. In PLD, an atomic pulse beam with a period t(0) were deposited instantaneously on a substrate, whereas in MBD, adatoms were deposited during a short time interval t(1) (0≤t(1)≤t(0)) within each period. If t(1)=0, MBD will be identical to PLD and, if t(1)=t(0), MBD will become usual molecular beam epitaxy (MBE). Specifically, logarithmic scaling was investigated for the nucleation density reported for PLD, and the scaling of island density was studied regarding the growth for 0

Equilibrium-restricted solid-on-solid growth model on fractal substrates.

The equilibrium-restricted solid-on-solid growth model on fractal substrates is studied by introducing a fractional Langevin equation. The growth exponent beta and the roughness exponent alpha defined, respectively, by the surface width via W approximately t(beta) and the saturated width via W(sat) approximately L(alpha), L being the system size, were obtained by a power-counting analysis, and the scaling relation 2alpha+d(f)=z(RW) was found to hold. The numerical simulation data on Sierpinski gasket, checkerboard fractal, and critical percolation cluster were found to agree well with the analytical predictions of the fractional Langevin equation.

Surface growth on diluted lattices by a restricted solid-on-solid model.

An influence of diluted sites on surface growth has been investigated, using the restricted solid-on-solid model. It was found that, with respect to equilibrium growth, the surface width and the saturated width exhibited universal power-law behaviors, i.e., W approximately t(beta) and W(sat) approximately L(zeta), regarding all cases with respect to the concentration of diluted sites x=1-p , with p being the occupation probability on each lattice site. For x < x(c) (=1-p(c), p(c) being the percolation threshold), the growth appeared to be similar to that of a regular lattice, both in two and three dimensions. For x=x(c), the growth yielded nontrivial exponents which were different from those on a regular lattice. In nonequilibrium growth, a considerable amount of diluted sites (x < or = x(c)) appeared to yield nonuniversal growth, unlike the case of a regular lattice. The cause of nonuniversal growth dynamics has been investigated, considering the growth on a backbone cluster and on lattices constructed with periodically and randomly diluted subcells.

Discontinuous phase transitions of conserved threshold transfer process with deterministic hopping.

The deterministic conserved threshold transfer process, which is a variant of the conserved threshold transfer process modified in a way as that hopping of a particle is to be deterministic, is proposed. The critical behavior of the model is investigated in one, two, and four dimensions. It is found that the order parameter yields a discontinuous transition; i.e., the transition appears to be first ordered in all dimensions considered. The origin of such a discontinuous transition is investigated, considering clustering of active sites and accumulation of critical sites just before the steady state is reached.

Structure optimization by conformational space annealing in an off-lattice protein model.

The optimization results by conformational space annealing are presented for an off-lattice protein model consisting of hydrophobic and hydrophilic residues in Fibonacci sequences. The ground-state energies found are lower than those reported in the literature. In addition, the ground-state conformations in three dimensions exhibit the important aspect of forming a single hydrophobic core in real proteins. The energy landscape for the population of local minima is also investigated.

Interfacial mixing in heteroepitaxial growth.

We investigate the growth of a film of some element B on a substrate made of another substance A in a model of molecular beam epitaxy. A vertical exchange mechanism (partial surfactant behavior) allows the A atoms to stay on the growing surface with a certain probability. Using kinetic Monte Carlo simulations as well as scaling arguments, the incorporation of the A 's into the growing B layer is investigated. Moreover, we develop a rate equation theory for this process. The concentration of A impurities decays in the B -film like (distance from the interface)(-1-beta), where beta approximately 0.5 for two-dimensional surfaces, approximately 0.8 in the one-dimensional case, and 1 in mean-field approximation. The power law is cut off exponentially at a characteristic thickness of the interdiffusion zone that depends on the rate of exchange of a B adatom with an A atom in the surface and on the diffusion length. Under certain conditions the interdiffusion zone is predicted to become narrower, if the growth temperature is increased.