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## Full-Text Articles in Physics

Opinion Formation On Adaptive Networks With Intensive Average Degree, Beate Schmittmann, Abhishek Mukhopadhyay

#### Opinion Formation On Adaptive Networks With Intensive Average Degree, Beate Schmittmann, Abhishek Mukhopadhyay

*Beate Schmittmann*

We study the evolution of binary opinions on a simple adaptive network of N nodes. At each time step, a randomly selected node updates its state (“opinion”) according to the majority opinion of the nodes that it is linked to; subsequently, all links are reassigned with probability p̃ (q̃ ) if they connect nodes with equal (opposite) opinions. In contrast to earlier work, we ensure that the average connectivity (“degree”) of each node is independent of the system size (“intensive”), by choosing p̃ and q̃ to be of O(1/N). Using simulations and analytic arguments, we determine the final steady ...

Competition Between Multiple Totally Asymmetric Simple Exclusion Processes For A Finite Pool Of Resources, L. Jonathan Cook, R. K. P. Zia, Beate Schmittmann

#### Competition Between Multiple Totally Asymmetric Simple Exclusion Processes For A Finite Pool Of Resources, L. Jonathan Cook, R. K. P. Zia, Beate Schmittmann

*Beate Schmittmann*

Using Monte Carlo simulations and a domain-wall theory, we discuss the effect of coupling several totally asymmetric simple exclusion processes (TASEPs) to a finite reservoir of particles. This simple model mimics directed biological transport processes in the presence of finite resources such as protein synthesis limited by a finite pool of ribosomes. If all TASEPs have equal length, we find behavior which is analogous to a single TASEP coupled to a finite pool. For the more generic case of chains with different lengths, several unanticipated regimes emerge. A generalized domain-wall theory captures our findings in good agreement with simulation results.

Opinion Dynamics On An Adaptive Random Network, I. J. Benczik, S. Z. Benczik, Beate Schmittmann, R. K. P. Zia

#### Opinion Dynamics On An Adaptive Random Network, I. J. Benczik, S. Z. Benczik, Beate Schmittmann, R. K. P. Zia

*Beate Schmittmann*

We revisit the classical model for voter dynamics in a two-party system with two basic modifications. In contrast to the original voter model studied in regular lattices, we implement the opinion formation process in a random network of agents in which interactions are no longer restricted by geographical distance. In addition, we incorporate the rapidly changing nature of the interpersonal relations in the model. At each time step, agents can update their relationships. This update is determined by their own opinion, and by their preference to make connections with individuals sharing the same opinion, or rather with opponents. In this ...

Inhomogeneous Exclusion Processes With Extended Objects: The Effect Of Defect Locations, J. J. Dong, Beate Schmittmann, R. K. P. Zia

#### Inhomogeneous Exclusion Processes With Extended Objects: The Effect Of Defect Locations, J. J. Dong, Beate Schmittmann, R. K. P. Zia

*Beate Schmittmann*

We study the effects of local inhomogeneities, i.e., slow sites of hopping rate q<1, in a totally asymmetric simple exclusion process for particles of size ℓ⩾1 (in units of the lattice spacing). We compare the simulation results of ℓ=1 and ℓ>1 and notice that the existence of local defects has qualitatively similar effects on the steady state. We focus on the stationary current as well as the density profiles. If there is only a single slow site in the system, we observe a significant dependence of the current on the location of the slow site for both ℓ=1 and ℓ>1 cases. When two slow sites are introduced, more intriguing phenomena emerge, e.g., dramatic decreases in the current when the two are close ...

Power Spectra Of The Total Occupancy In The Totally Asymmetric Simple Exclusion Process, D. `A. Adams, R. K. P. Zia, Beate Schmittmann

#### Power Spectra Of The Total Occupancy In The Totally Asymmetric Simple Exclusion Process, D. `A. Adams, R. K. P. Zia, Beate Schmittmann

*Beate Schmittmann*

As a solvable and broadly applicable model system, the totally asymmetric exclusion process enjoys iconic status in the theory of nonequilibrium phase transitions. Here, we focus on the time dependence of the total number of particles on a 1-dimensional open lattice and its power spectrum. Using both Monte Carlo simulations and analytic methods, we explore its behavior in different characteristic regimes. In the maximal current phase and on the coexistence line (between high and low density phases), the power spectrum displays algebraic decay, with exponents −1.62 and −2.00, respectively. Deep within the high and low density phases, we ...

Controlling Surface Morphologies By Time-Delayed Feedback, M. Block, Beate Schmittmann, E. Schöll

#### Controlling Surface Morphologies By Time-Delayed Feedback, M. Block, Beate Schmittmann, E. Schöll

*Beate Schmittmann*

We propose a method to control the roughness of a growing surface via a time-delayed feedback scheme. The method is very general and can be applied to a wide range of nonequilibrium growth phenomena, from solid-state epitaxy to tumor growth. Possible experimental realizations are suggested. As an illustration, we consider the Kardar-Parisi-Zhang equation [Phys. Rev. Lett. 56, 889 (1986)] in 1+1 dimensions and show that the effective growth exponent of the surface width can be stabilized at any desired value in the interval [0.25, 0.33], for a significant length of time.

Coarsening Of “Clouds” And Dynamic Scaling In A Far-From-Equilibrium Model System, D. A. Adams, Beate Schmittmann, R. K. P. Zia

#### Coarsening Of “Clouds” And Dynamic Scaling In A Far-From-Equilibrium Model System, D. A. Adams, Beate Schmittmann, R. K. P. Zia

*Beate Schmittmann*

A two-dimensional lattice gas of two species, driven in opposite directions by an external force, undergoes a jamming transition if the filling fraction is sufficiently high. Using Monte Carlo simulations, we investigate the growth of these jams (‘‘clouds’’), as the system approaches a nonequilibrium steady state from a disordered initial state. We monitor the dynamic structure factor S(kx,ky;t) and find that the kx=0 component exhibits dynamic scaling, of the form S(0,ky;t)=tβS̃ (kytα). Over a significant range of times, we observe excellent data collapse with α=1/2 and β=1. The effects ...

Strongly Anisotropic Roughness In Surfaces Driven By An Oblique Particle Flux, Beate Schmittmann, Gunner Pruessner, Hans-Karl Janssen

#### Strongly Anisotropic Roughness In Surfaces Driven By An Oblique Particle Flux, Beate Schmittmann, Gunner Pruessner, Hans-Karl Janssen

*Beate Schmittmann*

Using field theoretic renormalization, an MBE-type growth process with an obliquely incident influx of atoms is examined. The projection of the beam on the substrate plane selects a “parallel” direction, with rotational invariance restricted to the transverse directions. Depending on the behavior of an effective anisotropic surface tension, a line of second-order transitions is identified, as well as a line of potentially first-order transitions, joined by a multicritical point. Near the second-order transitions and the multicritical point, the surface roughness is strongly anisotropic. Four different roughness exponents are introduced and computed, describing the surface in different directions, in real or ...

Steady States Of A Nonequilibrium Lattice Gas, Edward Lyman, Beate Schmittmann

#### Steady States Of A Nonequilibrium Lattice Gas, Edward Lyman, Beate Schmittmann

*Beate Schmittmann*

We present a Monte Carlo study of a lattice gas driven out of equilibrium by a local hopping bias. Sites can be empty or occupied by one of two types of particles, which are distinguished by their response to the hopping bias. All particles interact via excluded volume and a nearest-neighbor attractive force. The main result is a phase diagram with three phases: a homogeneous phase and two distinct ordered phases. Continuous boundaries separate the homogeneous phase from the ordered phases, and a first-order line separates the two ordered phases. The three lines merge in a nonequilibrium bicritical point.

Exact Dynamics Of A Reaction-Diffusion Model With Spatially Alternating Rates, M. Mobilia, Beate Schmittmann, R. K. P. Zia

#### Exact Dynamics Of A Reaction-Diffusion Model With Spatially Alternating Rates, M. Mobilia, Beate Schmittmann, R. K. P. Zia

*Beate Schmittmann*

We present the exact solution for the full dynamics of a nonequilibrium spin chain and its dual reaction-diffusion model, for arbitrary initial conditions. The spin chain is driven out of equilibrium by coupling alternating spins to two thermal baths at different temperatures. In the reaction-diffusion model, this translates into spatially alternating rates for particle creation and annihilation, and even negative “temperatures” have a perfectly natural interpretation. Observables of interest include the magnetization, the particle density, and all correlation functions for both models. Two generic types of time dependence are found: if both temperatures are positive, the magnetization, density, and correlation ...

Anomalous Nucleation Far From Equilibrium, I. T. Georgiev, Beate Schmittmann, R. K. P. Zia

#### Anomalous Nucleation Far From Equilibrium, I. T. Georgiev, Beate Schmittmann, R. K. P. Zia

*Beate Schmittmann*

We present precision Monte Carlo data and analytic arguments for an asymmetric exclusion process, involving two species of particles driven in opposite directions on a 2×L lattice. To resolve a stark discrepancy between earlier simulation data and an analytic conjecture, we argue that the presence of a single macroscopic cluster is an intermediate stage of a complex nucleation process: in smaller systems, this cluster is destabilized while larger systems form multiple clusters. Both limits lead to exponential cluster size distributions, controlled by very different length scales.

Driven Diffusive Systems: How Steady States Depend On Dynamics, D. P. Landau, Wooseop Kwak, Beate Schmittmann

#### Driven Diffusive Systems: How Steady States Depend On Dynamics, D. P. Landau, Wooseop Kwak, Beate Schmittmann

*Beate Schmittmann*

In contrast to equilibrium systems, nonequilibrium steady states depend explicitly on the underlying dynamics. Using Monte Carlo simulations with Metropolis, Glauber, and heat bath rates, we illustrate this expectation for an Ising lattice gas, driven far from equilibrium by an “electric” field. While heat bath and Glauber rates generate essentially identical data for structure factors and two-point correlations, Metropolis rates give noticeably weaker correlations, as if the “effective” temperature were higher in the latter case. We also measure energy histograms and define a simple ratio which is exactly known and closely related to the Boltzmann factor for the equilibrium case ...

Stationary Correlations For A Far-From-Equilibrium Spin Chain, Beate Schmittmann, F. Schmüser

#### Stationary Correlations For A Far-From-Equilibrium Spin Chain, Beate Schmittmann, F. Schmüser

*Beate Schmittmann*

A kinetic one-dimensional Ising model on a ring evolves according to a generalization of Glauber rates, such that spins at even (odd) lattice sites experience a temperature Te (To). Detailed balance is violated so that the spin chain settles into a nonequilibrium stationary state, characterized by multiple interactions of increasing range and spin order. We derive the equations of motion for arbitrary correlation functions and solve them to obtain an exact representation of the steady state. Two nontrivial amplitudes reflect the sublattice symmetries; otherwise, correlations decay exponentially, modulo the periodicity of the ring. In the long-chain limit, they factorize into ...

Microscopic Kinetics And Time-Dependent Structure Factors, T. Aspelmeier, Beate Schmittmann, R. K. P. Zia

#### Microscopic Kinetics And Time-Dependent Structure Factors, T. Aspelmeier, Beate Schmittmann, R. K. P. Zia

*Beate Schmittmann*

The time evolution of structure factors (SF) in the disordering process of an initially phase-separated lattice depends crucially on the microscopic disordering mechanism, such as Kawasaki dynamics (KD) or vacancy-mediated disordering (VMD). Monte Carlo simulations show unexpected “dips” in the SFs. A phenomenological model is introduced to explain the dips in the odd SFs, and an analytical solution of KD is derived, in excellent agreement with simulations. The presence (absence) of dips in the even SFs for VMD (KD) marks a significant but not yet understood difference of the two dynamics.

Viability Of Competing Field Theories For The Driven Lattice Gas, Beate Schmittmann, H. K. Janssen, U. C. Tauber, R. K. P. Zia, K.-T. Leung, J. L. Cardy

#### Viability Of Competing Field Theories For The Driven Lattice Gas, Beate Schmittmann, H. K. Janssen, U. C. Tauber, R. K. P. Zia, K.-T. Leung, J. L. Cardy

*Beate Schmittmann*

It has recently been suggested that the driven lattice gas should be described by an alternate field theory in the limit of infinite drive. We review the original and the alternate field theory, invoking several well-documented key features of the microscopics. Since the alternate field theory fails to reproduce these characteristics, we argue that it cannot serve as a viable description of the driven lattice gas. Recent results, for the critical exponents associated with this theory, are reanalyzed and shown to be incorrect.

Universal Aspects Of Vacancy-Mediated Disordering Dynamics: The Effect Of External Fields, Wannapong Triampo, Timo Aspelmeier, Beate Schmittmann

#### Universal Aspects Of Vacancy-Mediated Disordering Dynamics: The Effect Of External Fields, Wannapong Triampo, Timo Aspelmeier, Beate Schmittmann

*Beate Schmittmann*

We investigate the disordering of an initially phase-segregated binary alloy, due to a highly mobile defect which couples to an electric or gravitational field. Using both mean-field and Monte Carlo methods, we show that the late stages of this process exhibit dynamic scaling, characterized by a set of exponents and scaling functions. A new scaling variable emerges, associated with the field. While the scaling functions carry information about the field and the boundary conditions, the exponents are universal. They can be computed analytically, in excellent agreement with simulation results.

Field-Induced Vacancy Localization In A Driven Lattice Gas: Scaling Of Steady States, M. Thies, Beate Schmittmann

#### Field-Induced Vacancy Localization In A Driven Lattice Gas: Scaling Of Steady States, M. Thies, Beate Schmittmann

*Beate Schmittmann*

With the help of Monte Carlo simulations and a mean-field theory, we investigate the ordered steady-state structures resulting from the motion of a single vacancy on a periodic lattice which is filled with two species of oppositely “charged” particles. An external field biases particle-vacancy exchanges according to the particle’s charge, subject to an excluded volume constraint. The steady state exhibits charge segregation, and the vacancy is localized at one of the two characteristic interfaces. Charge and hole density profiles, an appropriate order parameter, and the interfacial regions themselves exhibit characteristic scaling properties with system size and field strength. The ...

Structure Factors And Their Distributions In Driven Two-Species Models, G. Korniss, Beate Schmittmann

#### Structure Factors And Their Distributions In Driven Two-Species Models, G. Korniss, Beate Schmittmann

*Beate Schmittmann*

We study spatial correlations and structure factors in a three-state stochastic lattice gas, consisting of holes and two oppositely “charged” species of particles, subject to an “electric” field at zero total charge. The dynamics consists of two nearest-neighbor exchange processes, occurring on different times scales, namely, particle-hole and particle-particle exchanges. Using both Langevin equations and Monte Carlo simulations, we study the steady-state structure factors and correlation functions in the disordered phase, where density profiles are homogeneous. In contrast to equilibrium systems, the average structure factors here show a discontinuity singularity at the origin. The associated spatial correlation functions exhibit intricate ...

Frozen Disorder In A Driven System, Beate Schmittmann, K. E. Bassler

#### Frozen Disorder In A Driven System, Beate Schmittmann, K. E. Bassler

*Beate Schmittmann*

We investigate the effects of quenched disorder on the universal properties of a randomly driven Ising lattice gas. The Hamiltonian fixed point of the pure system becomes unstable in the presence of a quenched local bias, giving rise to a new fixed point which controls a novel universality class. We determine the associated scaling forms of correlation and response functions, quoting critical exponents to two-loop order in an expansion around the upper critical dimension dc=5.

Phase Transitions In Driven Bilayer Systems: A Monte Carlo Study, C. C. Hill, R. K. P. Zia, Beate Schmittmann

#### Phase Transitions In Driven Bilayer Systems: A Monte Carlo Study, C. C. Hill, R. K. P. Zia, Beate Schmittmann

*Beate Schmittmann*

We investigate the phase diagram of a system with two layers of an Ising lattice gas at half filling. In addition to the usual intralayer nearest neighbor attractive interaction, there is an interlayer potential J. Under equilibrium conditions, the phase diagram is symmetric under J→−J, though the ground states are different. The effects of imposing a uniform external drive, studied by simulation techniques, are dramatic. The mechanisms responsible for such behavior are discussed.

Critical Dynamics Of Nonconserved Ising-Like Systems, K. E. Bassler, Beate Schmittmann

#### Critical Dynamics Of Nonconserved Ising-Like Systems, K. E. Bassler, Beate Schmittmann

*Beate Schmittmann*

We show that the dynamical fixed point of Ising-like models, characterized by a single scalar, nonconserved ordering field, is stable near four dimensions with respect to all dynamic perturbations, including those of a nonequilibrium nature.

Spontaneous Structure Formation In Driven Systems With Two Species: Exact Solutions In A Mean-Field Theory, I. Vilfan, R. K. P. Zia, Beate Schmittmann

#### Spontaneous Structure Formation In Driven Systems With Two Species: Exact Solutions In A Mean-Field Theory, I. Vilfan, R. K. P. Zia, Beate Schmittmann

*Beate Schmittmann*

A stochastic lattice gas of particles, subject to an excluded volume constraint and to a uniform external driving field, is investigated. Using a mean-field theory for a system with equal number of oppositely charged particles, exact results are obtained. Focusing on the current-vs-density plot, we propose an explanation for the discontinuous transition found in earlier simulations. A critical value of the drive, below which this transition becomes continuous, is found. These results are supported by a bifurcation analysis, leading to an equation of motion for the amplitude of the soft mode.

Renormalization-Group Study Of A Hybrid Driven Diffusive System, K. E. Bassler, Beate Schmittmann

#### Renormalization-Group Study Of A Hybrid Driven Diffusive System, K. E. Bassler, Beate Schmittmann

*Beate Schmittmann*

We consider a d-dimensional stochastic lattice gas of interacting particles, diffusing under the influence of a short-ranged, attractive Ising Hamiltonian and a ‘‘hybrid’’ external field which is a superposition of a uniform and an annealed random drive, acting in orthogonal subspaces of dimensions one and m, respectively. Driven into a nonequilibrium steady state, the half-filled system phase segregates via a continuous transition at a field-dependent critical temperature. Using renormalization-group techniques, we show that its critical behavior falls into a new universality class with upper critical dimension dc=5-m, characterized by two distinct anisotropy exponents, which, like all other indices, are ...

Three-Point Correlation Functions In Uniformly And Randomly Driven Diffusive Systems, K. Hwang, Beate Schmittmann, R. K. P. Zia

#### Three-Point Correlation Functions In Uniformly And Randomly Driven Diffusive Systems, K. Hwang, Beate Schmittmann, R. K. P. Zia

*Beate Schmittmann*

Driven far away from equilibrium by both uniform and random external fields, a system of diffusing particles with short-range attractive forces displays many singular thermodynamic properties. Surprisingly, measuring pair correlations in lattice-gas models with saturation drives, we find little difference between the uniform and random cases, even though the underlying symmetries are quite distinct. Motivated by this puzzle, we study three-point correlations using both field-theoretic and simulation techniques. The continuum theory predicts the following: (a) The three-point function is nonzero only for the uniformly driven system; (b) it is odd under a parity transformation; and (c) there exists an infinite ...

Three-Point Correlations In Driven Diffusive Systems With Ising Symmetry, Beate Schmittmann, R. K. P. Zia

#### Three-Point Correlations In Driven Diffusive Systems With Ising Symmetry, Beate Schmittmann, R. K. P. Zia

*Beate Schmittmann*

For equilibrium systems with Ising symmetry, the three-point correlation function is always zero above criticality. When a lattice-gas version of this system is driven to a nonequilibrium steady state, this correlation becomes nontrivial. Its dominant large-scale behavior is found to be a consequence of both the manifest breaking of Ising symmetry by the driving force and the more subtle violation of the fluctuation-dissipation theorem.

Finger Formation In A Driven Diffusive System, D. H. Boal, Beate Schmittmann, R. K. P. Zia

#### Finger Formation In A Driven Diffusive System, D. H. Boal, Beate Schmittmann, R. K. P. Zia

*Beate Schmittmann*

A driven diffusive lattice gas is studied in a rectangular geometry: particles are fed in at one side and extracted at the other, after being swept through the system by a uniform driving field. Being periodic in the transverse direction, the lattice lies on the surface of a cylinder. The resulting nonequilibrium steady state depends strongly on this choice of boundary conditions. Both Monte Carlo and analytic techniques are employed to investigate the structure of typical configurations, the density profile, the steady-state current, and the nearest-neighbor correlations. As the temperature is lowered in a finite system, the simulations indicate a ...

Critical Properties Of A Randomly Driven Diffusive System, Beate Schmittmann, R. K. P. Zia

#### Critical Properties Of A Randomly Driven Diffusive System, Beate Schmittmann, R. K. P. Zia

*Beate Schmittmann*

We consider a system of interacting particles, diffusing under the influence of both thermal noise and a random, external electric field which acts in a subspace of m dimensions. In the nonequilibrium steady state, the net current is zero. When the interparticle interaction is short ranged and attractive, a second-order phase transition is expected. Analyzing this system in field-theoretic terms, we find the upper critical dimension to be 4-m and its behavior to fall outside the universality classes of the equilibrium Ising model and the usual driven diffusive system. A new fixed point and critical exponents are computed.

Phase Transitions In A Driven Lattice Gas With Repulsive Interactions, K.-T. Leung, Beate Schmittmann, R. K. P. Zia

#### Phase Transitions In A Driven Lattice Gas With Repulsive Interactions, K.-T. Leung, Beate Schmittmann, R. K. P. Zia

*Beate Schmittmann*

We study a lattice gas with repulsive nearest-neighbor interactions driven to steady state by an external electric field E. Using Monte Carlo techniques on a two-dimensional system, we find, in the E-T plane, a line of second-order transitions joining a line of first-order ones, at a point which is probably tricritical. From a field theoretical model, we show that the operator associated with E is naively irrelevant for critical behavior. This expectation is borne out by the Monte Carlo result β=(1/8.

Effects Of Pollution On Critical Population Dynamics, R. Kree, B. Schaub, Beate Schmittmann

#### Effects Of Pollution On Critical Population Dynamics, R. Kree, B. Schaub, Beate Schmittmann

*Beate Schmittmann*

We investigate the effects of pollution on a population that is on the brink of extinction. In the vicinity of the associated critical point, the temporal scales of the population density fluctuations are found to be completely governed by the diffusive behavior of the pollution density fluctuations. Moreover, the mean value of the population density is found to vanish with a larger power-law exponent in the presence of pollution density fluctuations. Results are obtained within a renormaliza- tion-group calculation to O(ε) (ε=4-d, d being the spatial dimension).

Effects Of Surfaces On Dynamic Percolation, H. K. Janssen, B. Schaub, Beate Schmittmann

#### Effects Of Surfaces On Dynamic Percolation, H. K. Janssen, B. Schaub, Beate Schmittmann

*Beate Schmittmann*

The general epidemic process, which is a stochastic multiparticle process belonging to the universality class of dynamic percolation, is studied in a semi-infinite geometry. Critical exponents characterizing the fractal properties are calculated to O(ε) (ε=6-d, where d is the spatial dimension) with use of renormalization-group techniques.