38 research outputs found

### Particle-hopping Models of Vehicular Traffic: Distributions of Distance Headways and Distance Between Jams

We calculate the distribution of the distance headways (i.e., the
instantaneous gap between successive vehicles) as well as the distribution of
instantaneous distance between successive jams in the Nagel-Schreckenberg (NS)
model of vehicular traffic. When the maximum allowed speed, $V_{max}$, of the
vehicles is larger than unity, over an intermediate range of densities of
vehicles, our Monte Carlo (MC) data for the distance headway distribution
exhibit two peaks, which indicate the coexistence of "free-flowing" traffic and
traffic jams. Our analytical arguments clearly rule out the possibility of
occurrence of more than one peak in the distribution of distance headways in
the NS model when $V_{max} = 1$ as well as in the asymmetric simple exclusion
process. Modifying and extending an earlier analytical approach for the NS
model with $V_{max} = 1$, and introducing a novel transfer matrix technique, we
also calculate the exact analytical expression for the distribution of distance
between the jams in this model; the corresponding distributions for $V_{max} >
1$ have been computed numerically through MC simulation.Comment: To appear in Physica

### Exact time-dependent correlation functions for the symmetric exclusion process with open boundary

As a simple model for single-file diffusion of hard core particles we
investigate the one-dimensional symmetric exclusion process. We consider an
open semi-infinite system where one end is coupled to an external reservoir of
constant density $\rho^\ast$ and which initially is in an non-equilibrium state
with bulk density $\rho_0$. We calculate the exact time-dependent two-point
density correlation function $C_{k,l}(t)\equiv -$ and the mean and variance of the integrated average net flux
of particles $N(t)-N(0)$ that have entered (or left) the system up to time $t$.
We find that the boundary region of the semi-infinite relaxing system is in a
state similar to the bulk state of a finite stationary system driven by a
boundary gradient. The symmetric exclusion model provides a rare example where
such behavior can be proved rigorously on the level of equal-time two-point
correlation functions. Some implications for the relaxational dynamics of
entangled polymers and for single-file diffusion in colloidal systems are
discussed.Comment: 11 pages, uses REVTEX, 2 figures. Minor typos corrected and reference
17 adde

### A Position-Space Renormalization-Group Approach for Driven Diffusive Systems Applied to the Asymmetric Exclusion Model

This paper introduces a position-space renormalization-group approach for
nonequilibrium systems and applies the method to a driven stochastic
one-dimensional gas with open boundaries. The dynamics are characterized by
three parameters: the probability $\alpha$ that a particle will flow into the
chain to the leftmost site, the probability $\beta$ that a particle will flow
out from the rightmost site, and the probability $p$ that a particle will jump
to the right if the site to the right is empty. The renormalization-group
procedure is conducted within the space of these transition probabilities,
which are relevant to the system's dynamics. The method yields a critical point
at $\alpha_c=\beta_c=1/2$,in agreement with the exact values, and the critical
exponent $\nu=2.71$, as compared with the exact value $\nu=2.00$.Comment: 14 pages, 4 figure

### Fluctuation Cumulant Behavior for the Field-Pulse Induced Magnetisation-Reversal Transition in Ising Models

The universality class of the dynamic magnetisation-reversal transition,
induced by a competing field pulse, in an Ising model on a square lattice,
below its static ordering temperature, is studied here using Monte Carlo
simulations. Fourth order cumulant of the order parameter distribution is
studied for different system sizes around the phase boundary region. The
crossing point of the cumulant (for different system sizes) gives the
transition point and the value of the cumulant at the transition point
indicates the universality class of the transition. The cumulant value at the
crossing point for low temperature and pulse width range is observed to be
significantly less than that for the static transition in the same
two-dimensional Ising model. The finite size scaling behaviour in this range
also indicates a higher correlation length exponent value. For higher
temperature and pulse width range, the transition seems to fall in a mean-field
like universality class.Comment: 5 pages, 8 eps figures, thoroughly revised manuscript with new
figures, accepted in Phys. Rev. E (2003

### First- and second-order phase transitions in a driven lattice gas with nearest-neighbor exclusion

A lattice gas with infinite repulsion between particles separated by $\leq 1$
lattice spacing, and nearest-neighbor hopping dynamics, is subject to a drive
favoring movement along one axis of the square lattice. The equilibrium (zero
drive) transition to a phase with sublattice ordering, known to be continuous,
shifts to lower density, and becomes discontinuous for large bias. In the
ordered nonequilibrium steady state, both the particle and order-parameter
densities are nonuniform, with a large fraction of the particles occupying a
jammed strip oriented along the drive. The relaxation exhibits features
reminiscent of models of granular and glassy materials.Comment: 8 pages, 5 figures; results due to bad random number generator
corrected; significantly revised conclusion

### Quantum phase transitions and thermodynamic properties in highly anisotropic magnets

The systems exhibiting quantum phase transitions (QPT) are investigated
within the Ising model in the transverse field and Heisenberg model with
easy-plane single-site anisotropy. Near QPT a correspondence between parameters
of these models and of quantum phi^4 model is established. A scaling analysis
is performed for the ground-state properties. The influence of the external
longitudinal magnetic field on the ground-state properties is investigated, and
the corresponding magnetic susceptibility is calculated. Finite-temperature
properties are considered with the use of the scaling analysis for the
effective classical model proposed by Sachdev. Analytical results for the
ordering temperature and temperature dependences of the magnetization and
energy gap are obtained in the case of a small ground-state moment. The forms
of dependences of observable quantities on the bare splitting (or magnetic
field) and renormalized splitting turn out to be different. A comparison with
numerical calculations and experimental data on systems demonstrating magnetic
and structural transitions (e.g., into singlet state) is performed.Comment: 46 pages, RevTeX, 6 figure

### Interfaces with a single growth inhomogeneity and anchored boundaries

The dynamics of a one dimensional growth model involving attachment and
detachment of particles is studied in the presence of a localized growth
inhomogeneity along with anchored boundary conditions. At large times, the
latter enforce an equilibrium stationary regime which allows for an exact
calculation of roughening exponents. The stochastic evolution is related to a
spin Hamiltonian whose spectrum gap embodies the dynamic scaling exponent of
late stages. For vanishing gaps the interface can exhibit a slow morphological
transition followed by a change of scaling regimes which are studied
numerically. Instead, a faceting dynamics arises for gapful situations.Comment: REVTeX, 11 pages, 9 Postscript figure

### Collective Diffusion and a Random Energy Landscape

Starting from a master equation in a quantum Hamiltonian form and a coupling
to a heat bath we derive an evolution equation for a collective hopping process
under the influence of a stochastic energy landscape. There results different
equations in case of an arbitrary occupation number per lattice site or in a
system under exclusion. Based on scaling arguments it will be demonstrated that
both systems belong below the critical dimension $d_c$ to the same universality
class leading to anomalous diffusion in the long time limit. The dynamical
exponent $z$ can be calculated by an $\epsilon = d_c-d$ expansion. Above the
critical dimension we discuss the differences in the diffusion constant for
sufficient high temperatures. For a random potential we find a higher mobility
for systems with exclusion.Comment: 15 pages, no figure

### Universality Class of Thermally Diluted Ising Systems at Criticality

The universality class of thermally diluted Ising systems, in which the
realization of the disposition of magnetic atoms and vacancies is taken from
the local distribution of spins in the pure original Ising model at
criticality, is investigated by finite size scaling techniques using the Monte
Carlo method. We find that the critical temperature, the critical exponents and
therefore the universality class of these thermally diluted Ising systems
depart markedly from the ones of short range correlated disordered systems. Our
results agree fairly well with theoretical predictions previously made by
Weinrib and Halperin for systems with long range correlated disorder.Comment: 7 pages, 6 figures, RevTe