arXiv subjects

Ronald Dickman

Publications and source records attributed to Ronald Dickman.

At least 55 records · Page 3Linked to original sources

arXiv2011

Conserved directed percolation: exact quasistationary distribution of small systems and Monte Carlo simulations

We study symmetric sleepy random walkers, a model exhibiting an absorbing-state phase transition in the conserved directed percolation (CDP) universality class. Unlike most examples of this class studied previously, this model possesses a continuously variable control parameter, facilitating analysis of critical properties. We study the model using two complementary approaches: analysis of the numerically exact quasistationary (QS) probability distribution on rings of up to 22 sites, and Monte Carlo simulation of systems of up to 32000 sites. The resulting estimates for critical exponents beta, beta/nu_perp, and z, and the moment ratio m_{211} = < rho^2 >/< rho >^2 (rho is the activity density), based on finite-size scaling at the critical point, are in agreement with previous results for the CDP universality class. We find, however, that the approach to the QS regime is characterized by a different value of the dynamic exponent z than found in the QS regime.

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arXiv2011

Pair contact process with diffusion of pairs

The pair contact process (PCP) is a nonequilibrium stochastic model which, like the basic contact process (CP), exhibits a phase transition to an absorbing state. The two models belong to the directed percolation (DP) universality class, despite the fact that the PCP possesses infinitely many absorbing configurations whereas the CP has but one. The critical behavior of the PCP with hopping by particles (PCPD) is as yet unclear. Here we study a version of the PCP in which nearest-neighbor particle {\it pairs} can hop but individual particles cannot. Using quasistationary simulations for three values of the diffusion probability ($D=0.1$, 0.5 and 0.9), we find convincing evidence of DP-like critical behavior.

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arXiv2010

Critical behavior of hard-core lattice gases: Wang-Landau sampling with adaptive windows

Critical properties of lattice gases with nearest-neighbor exclusion are investigated via the adaptive-window Wang-Landau algorithm on the square and simple cubic lattices, for which the model is known to exhibit an Ising-like phase transition. We study the particle density, order parameter, compressibility, Binder cumulant and susceptibility. Our results show that it is possible to estimate critical exponents using Wang-Landau sampling with adaptive windows. Finite-size-scaling analysis leads to results in fair agreement with exact values (in two dimensions) and numerical estimates (in three dimensions).

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arXiv2010

Phase diagram and critical behavior of the pair annihilation model

We study the critical behavior of the pair annihilation model (PAM) with diffusion in one, two and three dimensions, using the pair approximation (PA) and Monte Carlo simulation. Of principal interest is the dependence of the critical creation rate, lambda_c, on the diffusion probability D, in particular, whether survival is possible at arbitrarily small creation rates, for sufficiently rapid diffusion. Whilst the PA predicts that in any spatial dimension d \geq 1, lambda_c -> 0 at some diffusion probability D* < 1, Katori and Konno [Physica A {\bf 186}, 578 (1992)] showed rigorously that for d \leq 2, one has lambda_c > 0 for any D<1. Our simulation results are consistent with this theorem. In two dimensions, the extinction region becomes narrow as D approaches unity, following lambda_c \propto \exp[- \rm{const.}/(1-D)^γ], with gamma = 1.41(2). In three dimensions we find D* = 0.333(3). The simulation results confirm that the PAM belongs to the directed percolation universality class.

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arXiv2010

Asymmetric Exclusion Process in a System of Interacting Brownian Particles

We study a continuous-space version of the totally asymmetric simple exclusion process (TASEP), consisting of interacting Brownian particles subject to a driving force in a periodic external potential. Particles are inserted at the leftmost site at rate $α$, hop to the right at unit rate, and are removed at the rightmost site at rate $β$. Our study is motivated by recent experiments on colloidal particles in optical tweezer arrays. The external potential is of the form generated by such an array. Particles spend most of the time near potential minima, approximating the situation in the lattice gas; a short-range repulsive interaction prevents two particles from occupying the same potential well. A constant driving force, representing Stokes drag on particles suspended in a moving fluid, leads to biased motion. Our results for the density profile and current, obtained via numerical integration of the Langevin equation and dynamic Monte Carlo simulations, indicate that the continuous-space model exhibits phase transitions analogous to those observed in the lattice model. The correspondence is not exact, however, due to the lack of particle-hole symmetry in our model.

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arXiv2009

On the absorbing-state phase transition in the one-dimensional triplet creation model

We study the lattice reaction diffusion model 3A -> 4A, A -> 0 (``triplet creation") using numerical simulations and n-site approximations. The simulation results provide evidence of a discontinuous phase transition at high diffusion rates. In this regime the order parameter appears to be a discontinuous function of the creation rate; no evidence of a stable interface between active and absorbing phases is found. Based on an effective mapping to a modified compact directed percolation process, shall nevertheless argue that the transition is continuous, despite the seemingly discontinuous phase transition suggested by studies of finite systems.

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arXiv2009

Diffusion in stochastic sandpiles

We study diffusion of particles in large-scale simulations of one-dimensional stochastic sandpiles, in both the restricted and unrestricted versions. The results indicate that the diffusion constant scales in the same manner as the activity density, so that it represents an alternative definition of an order parameter. The critical behavior of the unrestricted sandpile is very similar to that of its restricted counterpart, including the fact that a data collapse of the order parameter as a function of the particle density is only possible over a very narrow interval near the critical point. We also develop a series expansion, in inverse powers of the density. for the collective diffusion coefficient in a variant of the stochastic sandpile in which the toppling rate at a site with $n$ particles is $n(n-1)$, and compare the theoretical prediction with simulation results.

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arXiv2009

Contact process with mobile disorder

I study the absorbing-state phase transition in the one-dimensional contact process with mobile disorder. In this model the dilution sites, though permanently inactive, diffuse freely, exchanging positions with the other sites, which host a basic contact process. Even though the disorder variables are not quenched, the critical behavior is affected: the critical exponents delta and z, the ratio beta/nu_perp and the moment ratio m= /rho^2 take values different from those of directed percolation, and appear to vary with the vacancy diffusion rate. While the survival probability starting from a single active seed follows the usual scaling, P(t) ~ t^{-delta}, at the critical point, the mean number of active sites and mean-square spread grow more slowly than power laws. The critical creation rate increases with the vacancy density v and diverges at a value v_c < 1. The scaling behavior at this point appears to be simpler than for smaller vacancy densities.

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arXiv2008

Two-dimensional lattice polymers: adaptive windows simulations

We report a numerical study of self-avoiding polymers on the square lattice, including an attractive potential between nonconsecutive monomers. Using Wang-Landau sampling (WLS) with adaptive windows, we obtain the density of states for chains of up to N=300 monomers and associated thermodynamic quantities. The method enables one to simulate accurately the low-temperature regime, which is virtually inaccessible using traditional methods. Instead of defining fixed energy windows, as in usual WLS, this method uses windows with boundaries that depend on the set of energy values on which the histogram is flat at a given stage of the simulation. Shifting the windows each time the modification factor $f$ is reduced, we eliminate border effects that arise in simulations using fixed windows.

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arXiv2008

Contact process on a Voronoi triangulation

We study the continuous absorbing-state phase transition in the contact process on the Voronoi-Delaunay lattice. The Voronoi construction is a natural way to introduce quenched coordination disorder in lattice models. We simulate the disordered system using the quasistationary simulation method and determine its critical exponents and moment ratios. Our results suggest that the critical behavior of the disordered system is unchanged with respect to that on a regular lattice, i.e., that of directed percolation.

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arXiv2008

Improving Wang-Landau sampling with adaptive windows

Wang-Landau sampling (WLS) of large systems requires dividing the energy range into "windows" and joining the results of simulations in each window. The resulting density of states (and associated thermodynamic functions) are shown to suffer from boundary effects in simulations of lattice polymers and the five-state Potts model. Here, we implement WLS using adaptive windows. Instead of defining fixed energy windows (or windows in the energy-magnetization plane for the Potts model), the boundary positions depend on the set of energy values on which the histogram is flat at a given stage of the simulation. Shifting the windows each time the modification factor f is reduced, we eliminate border effects that arise in simulations using fixed windows. Adaptive windows extend significantly the range of system sizes that may be studied reliably using WLS.

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arXiv2007

Absorbing-state phase transitions: exact solutions of small systems

I derive precise results for absorbing-state phase transitions using exact (numerically determined) quasistationary probability distributions for small systems. Analysis of the contact process on rings of 23 or fewer sites yields critical properties (control parameter, order-parameter ratios, and critical exponents z and beta/nu_perp) with an accuracy of better than 0.1%; for the exponent nu_perp the accuracy is about 0.5%. Good results are also obtained for the pair contact process.

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arXiv2007

Particle redistribution and slow decay of correlations in hard-core fluids on a half-driven ladder

We study driven particle systems with excluded volume interactions on a two-lane ladder with periodic boundaries, using Monte Carlo simulation, cluster mean-field theory, and numerical solution of the master equation. Particles in one lane are subject to a drive that forbids motion along one direction, while in the other lane the motion is unbiased; particles may jump between lanes. Despite the symmetry of the rates for transitions between lanes, the associated particle densities are unequal: at low densities there is an excess of particles in the undriven lane, while at higher densities the tendency is reversed. Similar results are found for an off-lattice model. We quantify the reduction in the stationary entropy caused by the drive. The stationary two-point correlation functions are found to decay algebraically, both on- and off-lattice. In the latter case the exponent governing the decay varies continuously with the density.

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arXiv2006

Diffusive epidemic process: theory and simulation

We study the continuous absorbing-state phase transition in the one-dimensional diffusive epidemic process via mean-field theory and Monte Carlo simulation. In this model, particles of two species (A and B) hop on a lattice and undergo reactions B -> A and A + B -> 2B; the total particle number is conserved. We formulate the model as a continuous-time Markov process described by a master equation. A phase transition between the (absorbing) B-free state and an active state is observed as the parameters (reaction and diffusion rates, and total particle density) are varied. Mean-field theory reveals a surprising, nonmonotonic dependence of the critical recovery rate on the diffusion rate of B particles. A computational realization of the process that is faithful to the transition rates defining the model is devised, allowing for direct comparison with theory. Using the quasi-stationary simulation method we determine the order parameter and the survival time in systems of up to 4000 sites. Due to strong finite-size effects, the results converge only for large system sizes. We find no evidence for a discontinuous transition. Our results are consistent with the existence of three distinct universality classes, depending on whether A particles diffusive more rapidly, less rapidly, or at the same rate as B particles.

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arXiv2006

Moment ratios for the pair contact process with diffusion

We study the continuous absorbing-state phase transition in the one-dimensional pair contact process with diffusion (PCPD). In previous studies [Dickman and de Menezes, Phys. Rev. E, 66 045101(R) (2002)], the critical point moment ratios of the order parameter showed anomalous behavior, growing with system size rather than taking universal values, as expected. Using the quasistationary simulation method we determine the moments of the order parameter up to fourth order at the critical point, in systems of up to 40960 sites. Due to strong finite-size effects, the ratios converge only for large system sizes. Moment ratios and associated order-parameter histograms are compared with those of directed percolation. We also report an improved estimate [p_c =0.077092(1)] for the nondiffusive pair contact process.

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arXiv2006

Restricted sandpile revisited

I report large-scale Monte Carlo studies of a one-dimensional height-restricted stochastic sandpile using the quasistationary simulation method. Results for systems of up to 50 000 sites yield estimates for critical exponents that differ significantly from those obtained using smaller systems, but are consistent with recent predictions derived from a Langevin equation for stochastic sandpiles [Ramasco et al., Phys. Rev. E{\bf 69}, 045105(R) (2004)]. This suggests that apparent violations of universality in one-dimensional sandpiles are due to strong corrections to scaling and finite-size effects.

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arXiv2006

Quasi-stationary simulation: the subcritical contact process

We apply the recently devised quasi-stationary simulation method to study the lifetime and order parameter of the contact process in the subcritical phase. This phase is not accessible to other methods because virtually all realizations of the process fall into the absorbing state before the quasi-stationary regime is attained. With relatively modest simulations, the method yields an estimate of the critical exponent nu_|| with a precision of 0.5%.

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arXiv2005

Functional-integral based perturbation theory for the Malthus-Verhulst process

We apply a functional-integral formalism for Markovian birth and death processes to determine asymptotic corrections to mean-field theory in the Malthus-Verhulst process (MVP). Expanding about the stationary mean-field solution, we identify an expansion parameter that is small in the limit of large mean population, and derive a diagrammatic expansion in powers of this parameter. The series is evaluated to fifth order using computational enumeration of diagrams. Although the MVP has no stationary state, we obtain good agreement with the associated {\it quasi-stationary} values for the moments of the population size, provided the mean population size is not small. We compare our results with those of van Kampen's $Ω$-expansion, and apply our method to the MVP with input, for which a stationary state does exist.

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