3,779 research outputs found

### Two-way traffic flow: exactly solvable model of traffic jam

We study completely asymmetric 2-channel exclusion processes in 1 dimension.
It describes a two-way traffic flow with cars moving in opposite directions.
The interchannel interaction makes cars slow down in the vicinity of
approaching cars in other lane. Particularly, we consider in detail the system
with a finite density of cars on one lane and a single car on the other one.
When the interchannel interaction reaches a critical value, traffic jam
occurs, which turns out to be of first order phase transition. We derive exact
expressions for the average velocities, the current, the density profile and
the $k$- point density correlation functions. We also obtain the exact
probability of two cars in one lane being distance $R$ apart, provided there is
a finite density of cars on the other lane, and show the two cars form a weakly
bound state in the jammed phase.Comment: 17 pages, Latex, ioplppt.sty, 11 ps figure

### Persistence in the Zero-Temperature Dynamics of the Diluted Ising Ferromagnet in Two Dimensions

The non-equilibrium dynamics of the strongly diluted random-bond Ising model
in two-dimensions (2d) is investigated numerically.
The persistence probability, P(t), of spins which do not flip by time t is
found to decay to a non-zero, dilution-dependent, value $P(\infty)$. We find
that $p(t)=P(t)-P(\infty)$ decays exponentially to zero at large times.
Furthermore, the fraction of spins which never flip is a monotonically
increasing function over the range of bond-dilution considered. Our findings,
which are consistent with a recent result of Newman and Stein, suggest that
persistence in disordered and pure systems falls into different classes.
Furthermore, its behaviour would also appear to depend crucially on the
strength of the dilution present.Comment: some minor changes to the text, one additional referenc

### Correlation functions of the One-Dimensional Random Field Ising Model at Zero Temperature

We consider the one-dimensional random field Ising model, where the spin-spin
coupling, $J$, is ferromagnetic and the external field is chosen to be $+h$
with probability $p$ and $-h$ with probability $1-p$. At zero temperature, we
calculate an exact expression for the correlation length of the quenched
average of the correlation function $\langle s_0 s_n \rangle - \langle s_0
\rangle \langle s_n \rangle$ in the case that $2J/h$ is not an integer. The
result is a discontinuous function of $2J/h$. When $p = {1 \over 2}$, we also
place a bound on the correlation length of the quenched average of the
correlation function $\langle s_0 s_n \rangle$.Comment: 12 pages (Plain TeX with one PostScript figure appended at end), MIT
CTP #220

### Directed polymer in a random medium of dimension 1+1 and 1+3: weights statistics in the low-temperature phase

We consider the low-temperature $T<T_c$ disorder-dominated phase of the
directed polymer in a random potentiel in dimension 1+1 (where $T_c=\infty$)
and 1+3 (where $T_c<\infty$). To characterize the localization properties of
the polymer of length $L$, we analyse the statistics of the weights $w_L(\vec
r)$ of the last monomer as follows. We numerically compute the probability
distributions $P_1(w)$ of the maximal weight $w_L^{max}= max_{\vec r} [w_L(\vec
r)]$, the probability distribution $\Pi(Y_2)$ of the parameter $Y_2(L)=
\sum_{\vec r} w_L^2(\vec r)$ as well as the average values of the higher order
moments $Y_k(L)= \sum_{\vec r} w_L^k(\vec r)$. We find that there exists a
temperature $T_{gap}<T_c$ such that (i) for $T<T_{gap}$, the distributions
$P_1(w)$ and $\Pi(Y_2)$ present the characteristic Derrida-Flyvbjerg
singularities at $w=1/n$ and $Y_2=1/n$ for $n=1,2..$. In particular, there
exists a temperature-dependent exponent $\mu(T)$ that governs the main
singularities $P_1(w) \sim (1-w)^{\mu(T)-1}$ and $\Pi(Y_2) \sim
(1-Y_2)^{\mu(T)-1}$ as well as the power-law decay of the moments $\bar{Y_k(i)} \sim 1/k^{\mu(T)}$. The exponent $\mu(T)$ grows from the value
$\mu(T=0)=0$ up to $\mu(T_{gap}) \sim 2$. (ii) for $T_{gap}<T<T_c$, the
distribution $P_1(w)$ vanishes at some value $w_0(T)<1$, and accordingly the
moments $\bar{Y_k(i)}$ decay exponentially as $(w_0(T))^k$ in $k$. The
histograms of spatial correlations also display Derrida-Flyvbjerg singularities
for $T<T_{gap}$. Both below and above $T_{gap}$, the study of typical and
averaged correlations is in full agreement with the droplet scaling theory.Comment: 13 pages, 29 figure

### Number and length of attractors in a critical Kauffman model with connectivity one

The Kauffman model describes a system of randomly connected nodes with
dynamics based on Boolean update functions. Though it is a simple model, it
exhibits very complex behavior for "critical" parameter values at the boundary
between a frozen and a disordered phase, and is therefore used for studies of
real network problems. We prove here that the mean number and mean length of
attractors in critical random Boolean networks with connectivity one both
increase faster than any power law with network size. We derive these results
by generating the networks through a growth process and by calculating lower
bounds.Comment: 4 pages, no figure, no table; published in PR

### Zero Temperature Dynamics of the Weakly Disordered Ising Model

The Glauber dynamics of the pure and weakly disordered random-bond 2d Ising
model is studied at zero-temperature. A single characteristic length scale,
$L(t)$, is extracted from the equal time correlation function. In the pure
case, the persistence probability decreases algebraically with the coarsening
length scale. In the disordered case, three distinct regimes are identified: a
short time regime where the behaviour is pure-like; an intermediate regime
where the persistence probability decays non-algebraically with time; and a
long time regime where the domains freeze and there is a cessation of growth.
In the intermediate regime, we find that $P(t)\sim L(t)^{-\theta'}$, where
$\theta' = 0.420\pm 0.009$. The value of $\theta'$ is consistent with that
found for the pure 2d Ising model at zero-temperature. Our results in the
intermediate regime are consistent with a logarithmic decay of the persistence
probability with time, $P(t)\sim (\ln t)^{-\theta_d}$, where $\theta_d =
0.63\pm 0.01$.Comment: references updated, very minor amendment to abstract and the
labelling of figures. To be published in Phys Rev E (Rapid Communications), 1
March 199

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