4,410 research outputs found

### Hierarchic trees with branching number close to one: noiseless KPZ equation with additional linear term for imitation of 2-d and 3-d phase transitions.

An imitation of 2d field theory is formulated by means of a model on the
hierarhic tree (with branching number close to one) with the same potential and
the free correlators identical to 2d correlators ones.
Such a model carries on some features of the original model for certain scale
invariant theories. For the case of 2d conformal models it is possible to
derive exact results. The renormalization group equation for the free energy is
noiseless KPZ equation with additional linear term.Comment: latex, 5 page

### 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

### Large Deviation Function of the Partially Asymmetric Exclusion Process

The large deviation function obtained recently by Derrida and Lebowitz for
the totally asymmetric exclusion process is generalized to the partially
asymmetric case in the scaling limit. The asymmetry parameter rescales the
scaling variable in a simple way. The finite-size corrections to the universal
scaling function and the universal cumulant ratio are also obtained to the
leading order.Comment: 10 pages, 2 eps figures, minor changes, submitted to PR

### 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

### Spectral Degeneracies in the Totally Asymmetric Exclusion Process

We study the spectrum of the Markov matrix of the totally asymmetric
exclusion process (TASEP) on a one-dimensional periodic lattice at ARBITRARY
filling. Although the system does not possess obvious symmetries except
translation invariance, the spectrum presents many multiplets with degeneracies
of high order. This behaviour is explained by a hidden symmetry property of the
Bethe Ansatz. Combinatorial formulae for the orders of degeneracy and the
corresponding number of multiplets are derived and compared with numerical
results obtained from exact diagonalisation of small size systems. This
unexpected structure of the TASEP spectrum suggests the existence of an
underlying large invariance group.
Keywords: ASEP, Markov matrix, Bethe Ansatz, Symmetries.Comment: 19 pages, 1 figur

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