arXiv subjects

Ronald Dickman

Publications and source records attributed to Ronald Dickman.

At least 37 records · Page 2Linked to original sources

arXiv2016

Phase coexistence far from equilibrium

Investigation of simple far-from-equilibrium systems exhibiting phase separation leads to the conclusion that phase coexistence is not well defined in this context. This is because the properties of the coexisting nonequilibrium systems depend on how they are placed in contact, as verified in the driven lattice gas with attractive interactions, and in the two-temperature lattice gas, under (a) weak global exchange between uniform systems, and (b) phase-separated (nonuniform) systems. Thus, far from equilibrium, the notions of universality of phase coexistence (i.e., independence of how systems exchange particles and/or energy), and of phases with intrinsic properties (independent of their environment) are lost.

cond-mat.stat-mech↗

arXiv2015

Griffiths phases and localization in hierarchical modular networks

We study variants of hierarchical modular network models suggested by Kaiser and Hilgetag [Frontiers in Neuroinformatics, 4 (2010) 8] to model functional brain connectivity, using extensive simulations and quenched mean-field theory (QMF), focusing on structures with a connection probability that decays exponentially with the level index. Such networks can be embedded in two-dimensional Euclidean space. We explore the dynamic behavior of the contact process (CP) and threshold models on networks of this kind, including hierarchical trees. While in the small-world networks originally proposed to model brain connectivity, the topological heterogeneities are not strong enough to induce deviations from mean-field behavior, we show that a Griffiths phase can emerge under reduced connection probabilities, approaching the percolation threshold. In this case the topological dimension of the networks is finite, and extended regions of bursty, power-law dynamics are observed. Localization in the steady state is also shown via QMF. We investigate the effects of link asymmetry and coupling disorder, and show that localization can occur even in small-world networks with high connectivity in case of link disorder.

cond-mat.dis-nn↗

arXiv2014

Phase diagram of the symbiotic two-species contact process

We study the two-species symbiotic contact process (2SCP), recently proposed in [de Oliveira, Santos and Dickman, Phys. Rev. E {\bf 86}, 011121 (2012)] . In this model, each site of a lattice may be vacant or host single individuals of species A and/or B. Individuals at sites with both species present interact in a symbiotic manner, having a reduced death rate, $μ< 1$. Otherwise, the dynamics follows the rules of the basic CP, with individuals reproducing to vacant neighbor sites at rate $λ$ and dying at a rate of unity. We determine the full phase diagram in the $λ-μ$ plane in one and two dimensions by means of exact numerical quasistationary distributions, cluster approximations, and Monte Carlo simulations. We also study the effects of asymmetric creation rates and diffusion of individuals. In two dimensions, for sufficiently strong symbiosis (i.e., small $μ$), the absorbing-state phase transition becomes discontinuous for diffusion rates $D$ within a certain range. We report preliminary results on the critical surface and tricritical line in the $λ-μ-D$ space. Our results raise the possibility that strongly symbiotic associations of mobile species may be vulnerable to sudden extinction under increasingly adverse conditions.

q-bio.PE↗

arXiv2014

Failure of steady state thermodynamics in lattice gases under nonuniform drive

To be useful, steady state thermodynamics (SST) must be self-consistent and have predictive value. Although consistency of SST was recently verified for driven lattice gases under global weak exchange, I show here that it does not predict the coexisting densities in athermal stochastic lattice gases under a nonuniform drive. I consider the lattice gas with nearest-neighbor exclusion on the square lattice, with nearest-neighbor hopping (NNE dynamics), and with hopping to both nearest and next-nearest neighbors (NNE2 dynamics). Part of the system is subject to a drive $D$ that favors hopping along one direction, while the other part is free of the drive. Thus the steady state represents coexistence between two subsystems, one far from equilibrium and the other in equilibrium, which exchange particles along the interfaces. The dimensionless chemical potential $μ^*(ρ,D) = μ/k_B T$ for the lattice gas with density $ρ$ is readily determined in studies of a uniform system. Under the nonuniform drive, however, equating the chemical potentials of the coexisting subsystems does not yield the coexisting densities. The steady state chemical potential is, moreover, different in the coexisting bulk regions, contrary to the basic principles of thermodynamics. These results cast serious doubt on the predictive value of SST.

cond-mat.stat-mech↗

arXiv2014

Activity, diffusion, and correlations in a two-dimensional conserved stochastic sandpile

We perform large-scale simulations of a two-dimensional restricted-height conserved stochastic sandpile, focusing on particle diffusion and mobility, and spatial correlations. Quasistationary (QS) simulations yield the critical particle density to high precision [$p_c = 0.7112687(2)$], and show that the diffusion constant scales in the same manner as the activity density, as found previously in the one-dimensional case. Short-time scaling is characterized by subdiffusive behavior (mean-square displacement $\sim t^γ$ with $γ< 1$), which is easily understood as a consequence of the initial decay of activity, $ρ(t) \sim t^{-δ}$, with $γ= 1- δ$. We verify that at criticality, the activity correlation function $C(r) \sim r^{-β/ν_\perp}$, as expected at an absorbing-state phase transition. Our results for critical exponents are consistent with, and somewhat more precise than, predictions derived from the Langevin equation for stochastic sandpiles in two dimensions.

cond-mat.stat-mech↗

arXiv2014

Intrinsic convergence properties of entropic sampling algorithms

We study the convergence of the density of states and thermodynamic properties in three flat-histogram simulation methods, the Wang-Landau (WL) algorithm, the 1/t algorithm, and tomographic sampling (TS). In the first case the refinement parameter f is rescaled (f -> f/2) each time the flat-histogram condition is satisfied, in the second f ~ 1/t after a suitable initial phase, while in the third f is constant (t corresponds to Monte Carlo time). To examine the intrinsic convergence properties of these methods, free of any complications associated with a specific model, we study a featureless entropy landscape, such that for each allowed energy E = 1,...,L, there is exactly one state, that is, g(E) = 1 for all E. Convergence of sampling corresponds to g(E,t) -> const. as t -> infinity, so that the standard deviation sigma_g of g over energy values is a measure of the overall sampling error. Neither the WL algorithm nor TS converge: in both cases sigma_g saturates at long times. In the 1/t algorithm, by contrast, sigma_g decays \propto 1/\sqrt{t}. Modified TS and 1/t procedures, in which f \propto 1/t^alpha, converge for alpha values between 0 and 1. There are two essential facets to convergence of flat-histogram methods: elimination of initial errors in g(E), and correction of the sampling noise accumulated during the process. For a simple example, we demonstrate analytically, using a Langevin equation, that both kinds of errors can be eliminated, asymptotically, if f ~ 1/t^alpha with 0 < α\leq 1. Convergence is optimal for alpha = 1. For alpha \leq 0 the sampling noise never decays, while for alpha > 1 the initial error is never completely eliminated.

cond-mat.stat-mech↗

arXiv2014

Inconsistencies in steady state thermodynamics

We address the issue of extending thermodynamics to nonequilibrium steady states. Using driven stochastic lattice gases, we ask whether consistent definitions of an effective chemical potential mu, and an effective temperature T_e, are possible. mu and T_e are determined via coexistence, i.e., zero flux of particles and energy between the driven system and a reservoir. In the lattice gas with nearest-neighbor exclusion, temperature is not relevant, and we find that the effective chemical potential, a function of density and drive strength, satisfies the zeroth law, and correctly predicts the densities of coexisting systems. In the Katz-Lebowitz-Spohn driven lattice gas both mu and T_e need to be defined. We show analytically that in this case the zeroth law is violated for Metropolis exchange rates, and determine the size of the violations numerically. The zeroth law appears to be violated for generic exchange rates. Remarkably, the system-reservoir coupling proposed by Sasa and Tasaki [J. Stat. Phys. 125, 125 (2006)], is free of inconsistencies, and the zeroth law holds. This is because the rate depends only on the state of the donor system, and is independent of that of the acceptor.

cond-mat.stat-mech↗

arXiv2013

Survival of the Scarcer in Space

The dynamics leading to extinction or coexistence of competing species is of great interest in ecology and related fields. Recently a model of intra- and interspecific competition between two species was proposed by Gabel et al. [Phys. Rev. E 87 (2013) 010101], in which the scarcer species (i.e., with smaller stationary population size) can be more resistant to extinction when it holds a competitive advantage; the latter study considered populations without spatial variation. Here we verify this phenomenon in populations distributed in space. We extend the model of Gabel et al. to a d-dimensional lattice, and study its population dynamics both analytically and numerically. Survival of the scarcer in space is verified for situations in which the more competitive species is closer to the threshold for extinction than is the less competitive species, when considered in isolation. The conditions for survival of the scarcer species, as obtained applying renormalization group analysis and Monte Carlo simulation, differ in detail from those found in the spatially homogeneous case. Simulations highlight the speed of invasion waves in determining the survival times of the competing species.

q-bio.PE↗

arXiv2013

Conserved sandpile with a variable height restriction

We study a restricted-height version of the one-dimensional Oslo sandpile with conserved density, using periodic boundary conditions. Each site has a limiting height which can be either two or three. When a site reaches its limiting height it becomes active and may topple, loosing two particles, which move randomly to nearest-neighbor sites. After a site topples it is randomly assigned a new limiting height. We study the model using mean-field theory and Monte Carlo simulation, focusing on the quasi-stationary state, in which the number of active sites fluctuates about a stationary value. Using finite-size scaling analysis, we determine the critical particle density and associated critical exponents.

cond-mat.stat-mech↗

arXiv2012

Analysis of an information-theoretic model for communication

We study the cost-minimization problem posed by Ferrer i Cancho and Solé in their model of communication that aimed at explaining the origin of Zipf's law [PNAS 100, 788 (2003)]. Direct analysis shows that the minimum cost is $\min {λ, 1-λ}$, where $λ$ determines the relative weights of speaker's and hearer's costs in the total, as shown in several previous works using different approaches. The nature and multiplicity of the minimizing solution changes discontinuously at $λ=1/2$, being qualitatively different for $λ< 1/2$, $λ> 1/2$, and $λ=1/2$. Zipf's law is found only in a vanishing fraction of the minimum-cost solutions at $λ= 1/2$ and therefore is not explained by this model. Imposing the further condition of equal costs yields distributions substantially closer to Zipf's law, but significant differences persist. We also investigate the solutions reached by the previously used minimization algorithm and find that they correctly recover global minimum states at the transition.

cond-mat.stat-mech↗

arXiv2012

A symbiotic two-species contact process

We study a contact process (CP) with two species that interact in a symbiotic manner. In our model, each site of a lattice may be vacant or host individuals of species A and/or B; multiple occupancy by the same species is prohibited. Symbiosis is represented by a reduced death rate, mu < 1, for individuals at sites with both species present. Otherwise, the dynamics is that of the basic CP, with creation (at vacant neighbor sites) at rate lambda and death of (isolated) individuals at a rate of unity. Mean-field theory and Monte Carlo simulation show that the critical creation rate, lambda_c (mu), is a decreasing function of mu, even though a single-species population must go extinct for lambda < lambda_c(1), the critical point of the basic CP. Extensive simulations yield results for critical behavior that are compatible with the directed percolation (DP) universality class, but with unusually strong corrections to scaling. A field-theoretical argument supports the conclusion of DP critical behavior. We obtain similar results for a CP with creation at second-neighbor sites and enhanced survival at first neighbors, in the form of an annihilation rate that decreases with the number of occupied first neighbors.

cond-mat.stat-mech↗

arXiv2012

Discontinuous phase transition in a dimer lattice gas

I study a dimer model on the square lattice with nearest-neighbor exclusion as the only interaction. Detailed simulations using tomographic entropic sampling show that as the chemical potential is varied, there is a strongly discontinuous phase transition, at which the particle density jumps by about 18% of its maximum value, 1/4. The transition is accompanied by the onset of orientational order, to an arrangement corresponding to the {1/2,0,1/2} structure identified by Phares et al. [Physica B {\bf 409}, 1096 (2011)] in a dimer model with {\it finite} repulsion at {\it fixed} density. Using finite-size scaling and Binder's cumulant, the expected scaling behavior at a discontinuous transition is verified in detail. The discontinuous transition can be understood qualitatively given that the model possesses eight equivalent maximum-density configurations, so that its coarse-grained description corresponds to that of the q=8 Potts model.

cond-mat.stat-mech↗

arXiv2012

An epidemic process mediated by a decaying diffusing signal

We study a stochastic epidemic model consisting of elements (organisms in a community or cells in tissue) with fixed positions, in which damage or disease is transmitted by diffusing agents ("signals") emitted by infected individuals. The signals decay as well as diffuse; since they are assumed to be produced in large numbers, the signal concentration is treated deterministically. The model, which includes four cellular states (susceptible, transformed, depleted, and removed), admits various interpretations: spread of an infection or infectious disease, or of damage in a tissue in which injured cells may themselves provoke further damage, and as a description of the so-called radiation-induced bystander effect, in which the signals are molecules capable of inducing cell damage and/or death in unirradiated cells. The model exhibits a continuous phase transition between spreading and nonspreading phases. We formulate two mean-field theory (MFT) descriptions of the model, one of which ignores correlations between the cellular state and the signal concentration, and another that treats such correlations in an approximate manner. Monte Carlo simulations of the spread of infection on the square lattice yield values for the critical exponents and the fractal dimension consistent with the dynamic percolation universality class.

q-bio.PE↗

arXiv2011

Systematic enumeration of configuration classes for entropic sampling of Ising models

We describe a systematic method for complete enumeration of configuration classes (CCs) of the spin-1/2 Ising model in the energy-magnetization plane. This technique is applied to the antiferromagnetic Ising model in an external magnetic field on the square lattice, which is simulated using the tomographic entropic sampling algorithm. We estimate the number of configurations, $Ω(E,m,L)$, and related microcanonical averages, for all allowed energies $E$ and magnetizations $m$ for $L = 10$ to 30, with $ΔL = 2$. With prior knowledge of the CCs, we can be sure that all allowed classes are sampled during the simulation. Complete enumeration of CCs also enables us to use the final estimate of $Ω(E,m,L)$ to obtain good initial estimates, $Ω_0(E,m,L')$, for successive system sizes ($L' > L$) through a two-dimensional interpolation. Using these results we calculate canonical averages of the thermodynamic quantities of interest as continuous functions of temperature $T$ and external field $h$. In addition, we determine the critical line in the $h$-$T$ plane using finite-size scaling analysis, and compare these results with several approximate theoretical expressions.

cond-mat.stat-mech↗

arXiv2011

An infinite-period phase transition versus nucleation in a stochastic model of collective oscillations

A lattice model of three-state stochastic phase-coupled oscillators has been shown by Wood et al (2006 Phys. Rev. Lett. 96 145701) to exhibit a phase transition at a critical value of the coupling parameter, leading to stable global oscillations. We show that, in the complete graph version of the model, upon further increase in the coupling, the average frequency of collective oscillations decreases until an infinite-period (IP) phase transition occurs, at which point collective oscillations cease. Above this second critical point, a macroscopic fraction of the oscillators spend most of the time in one of the three states, yielding a prototypical nonequilibrium example (without an equilibrium counterpart) in which discrete rotational (C_3) symmetry is spontaneously broken, in the absence of any absorbing state. Simulation results and nucleation arguments strongly suggest that the IP phase transition does not occur on finite-dimensional lattices with short-range interactions.

physics.bio-ph↗

arXiv2011

Complete high-precision entropic sampling

Monte Carlo simulations using entropic sampling to estimate the number of configurations of a given energy are a valuable alternative to traditional methods. We introduce {\it tomographic} entropic sampling, a scheme which uses multiple studies, starting from different regions of configuration space, to yield precise estimates of the number of configurations over the {\it full range} of energies, {\it without} dividing the latter into subsets or windows. Applied to the Ising model on the square lattice, the method yields the critical temperature to an accuracy of about 0.01%, and critical exponents to 1% or better. Predictions for systems sizes L=10 - 160, for the temperature of the specific heat maximum, and of the specific heat at the critical temperature, are in very close agreement with exact results. For the Ising model on the simple cubic lattice the critical temperature is given to within 0.003% of the best available estimate; the exponent ratios $β/ν$ and $γ/ν$ are given to within about 0.4% and 1%, respectively, of the literature values. In both two and three dimensions, results for the {\it antiferromagnetic} critical point are fully consistent with those of the ferromagnetic transition. Application to the lattice gas with nearest-neighbor exclusion on the square lattice again yields the critical chemical potential and exponent ratios $β/ν$ and $γ/ν$ to good precision.

cond-mat.stat-mech↗

arXiv2011

Contact process with sublattice symmetry breaking

We study a contact process with creation at first- and second-neighbor sites and inhibition at first neighbors, in the form of an annihilation rate that increases with the number of occupied first neighbors. Mean-field theory predicts three phases: inactive (absorbing), active symmetric, and active asymmetric, the latter exhibiting distinct sublattice densities on a bipartite lattice. These phases are separated by continuous transitions; the phase diagram is reentrant. Monte Carlo simulations in two dimensions verify these predictions qualitatively, except for a first-neighbor creation rate of zero. (In the latter case one of the phase transitions is discontinuous.) Our numerical results confirm that the symmetric-asymmetric transition belongs to the Ising universality class, and that the active-absorbing transition belongs to the directed percolation class, as expected from symmetry considerations.

cond-mat.stat-mech↗

arXiv2011

Glassy dynamics and hysteresis in a linear system of orientable hard rods

We study the dynamics of a one-dimensional fluid of orientable hard rectangles with a non-coarse-grained microscopic mechanism of facilitation. The length occupied by a rectangle depends on its orientation, which is coupled to an external field. The equilibrium properties of our model are essentially those of the Tonks gas, but at high densities, the orientational degrees of freedom become effectively frozen due to jamming. This is a simple analytically tractable model of glassy phase. Under a cyclic variation of the pressure, hysteresis is observed. Following a pressure quench, the orientational persistence exhibits a two-stage decay characteristic of glassy systems.

cond-mat.dis-nn↗