849 research outputs found
Dynamic wetting with two competing adsorbates
We study the dynamic properties of a model for wetting with two competing
adsorbates on a planar substrate. The two species of particles have identical
properties and repel each other. Starting with a flat interface one observes
the formation of homogeneous droplets of the respective type separated by
nonwet regions where the interface remains pinned. The wet phase is
characterized by slow coarsening of competing droplets. Moreover, in 2+1
dimensions an additional line of continuous phase transition emerges in the
bound phase, which separates an unordered phase from an ordered one. The
symmetry under interchange of the particle types is spontaneously broken in
this region and finite systems exhibit two metastable states, each dominated by
one of the species. The critical properties of this transition are analyzed by
numeric simulations.Comment: 11 pages, 12 figures, final version published in PR
The XX--model with boundaries. Part I: Diagonalization of the finite chain
This is the first of three papers dealing with the XX finite quantum chain
with arbitrary, not necessarily hermitian, boundary terms. This extends
previous work where the periodic or diagonal boundary terms were considered. In
order to find the spectrum and wave-functions an auxiliary quantum chain is
examined which is quadratic in fermionic creation and annihilation operators
and hence diagonalizable. The secular equation is in general complicated but
several cases were found when it can be solved analytically. For these cases
the ground-state energies are given. The appearance of boundary states is also
discussed and in view to the applications considered in the next papers, the
one and two-point functions are expressed in terms of Pfaffians.Comment: 56 pages, LaTeX, some minor correction
Criticality of natural absorbing states
We study a recently introduced ladder model which undergoes a transition
between an active and an infinitely degenerate absorbing phase. In some cases
the critical behaviour of the model is the same as that of the branching
annihilating random walk with species both with and without hard-core
interaction. We show that certain static characteristics of the so-called
natural absorbing states develop power law singularities which signal the
approach of the critical point. These results are also explained using random
walk arguments. In addition to that we show that when dynamics of our model is
considered as a minimum finding procedure, it has the best efficiency very
close to the critical point.Comment: 6 page
First order phase transition in a 1+1-dimensional nonequilibrium wetting process
A model for nonequilibrium wetting in 1+1 dimensions is introduced. It
comprises adsorption and desorption processes with a dynamics which generically
does not obey detailed balance. Depending on the rates of the dynamical
processes the wetting transition is either of first or second order. It is
found that the wet (unbound) and the non-wet (pinned) states coexist and are
both thermodynamically stable in a domain of the dynamical parameters which
define the model. This is in contrast with equilibrium transitions where
coexistence of thermodynamically stable states takes place only on the
transition line.Comment: 4 pages, RevTeX, including 4 eps figure
The universal behavior of one-dimensional, multi-species branching and annihilating random walks with exclusion
A directed percolation process with two symmetric particle species exhibiting
exclusion in one dimension is investigated numerically. It is shown that if the
species are coupled by branching (, ) a continuous phase
transition will appear at zero branching rate limit belonging to the same
universality class as that of the dynamical two-offspring (2-BARW2) model. This
class persists even if the branching is biased towards one of the species. If
the two systems are not coupled by branching but hard-core interaction is
allowed only the transition will occur at finite branching rate belonging to
the usual 1+1 dimensional directed percolation class.Comment: 3 pages, 3 figures include
Matrix Product Ground States for Asymmetric Exclusion Processes with Parallel Dynamics
We show in the example of a one-dimensional asymmetric exclusion process that
stationary states of models with parallel dynamics may be written in a matrix
product form. The corresponding algebra is quadratic and involves three
different matrices. Using this formalism we prove previous conjectures for the
equal-time correlation functions of the model.Comment: LaTeX, 8 pages, one postscript figur
Multicomponent binary spreading process
I investigate numerically the phase transitions of two-component
generalizations of binary spreading processes in one dimension. In these models
pair annihilation: AA->0, BB->0, explicit particle diffusion and binary pair
production processes compete with each other. Several versions with spatially
different productions have been explored and shown that for the cases: 2A->3A,
2B->3B and 2A->2AB, 2B->2BA a phase transition occurs at zero production rate
(), that belongs to the class of N-component, asymmetric branching
and annihilating random walks, characterized by the order parameter exponent
. In the model with particle production: AB->ABA, BA-> BAB a phase
transition point can be located at that belongs to the class
of the one-component binary spreading processes.Comment: 5 pages, 5 figure
Branching and annihilating Levy flights
We consider a system of particles undergoing the branching and annihilating
reactions A -> (m+1)A and A + A -> 0, with m even. The particles move via
long-range Levy flights, where the probability of moving a distance r decays as
r^{-d-sigma}. We analyze this system of branching and annihilating Levy flights
(BALF) using field theoretic renormalization group techniques close to the
upper critical dimension d_c=sigma, with sigma<2. These results are then
compared with Monte-Carlo simulations in d=1. For sigma close to unity in d=1,
the critical point for the transition from an absorbing to an active phase
occurs at zero branching. However, for sigma bigger than about 3/2 in d=1, the
critical branching rate moves smoothly away from zero with increasing sigma,
and the transition lies in a different universality class, inaccessible to
controlled perturbative expansions. We measure the exponents in both
universality classes and examine their behavior as a function of sigma.Comment: 9 pages, 4 figure
Finite Dimensional Representations of the Quadratic Algebra: Applications to the Exclusion Process
We study the one dimensional partially asymmetric simple exclusion process
(ASEP) with open boundaries, that describes a system of hard-core particles
hopping stochastically on a chain coupled to reservoirs at both ends. Derrida,
Evans, Hakim and Pasquier [J. Phys. A 26, 1493 (1993)] have shown that the
stationary probability distribution of this model can be represented as a trace
on a quadratic algebra, closely related to the deformed oscillator-algebra. We
construct all finite dimensional irreducible representations of this algebra.
This enables us to compute the stationary bulk density as well as all
correlation lengths for the ASEP on a set of special curves of the phase
diagram.Comment: 18 pages, Latex, 1 EPS figur
Phase transitions in nonequilibrium d-dimensional models with q absorbing states
A nonequilibrium Potts-like model with absorbing states is studied using
Monte Carlo simulations. In two dimensions and the model exhibits a
discontinuous transition. For the three-dimensional case and the model
exhibits a continuous, transition with (mean-field). Simulations are
inconclusive, however, in the two-dimensional case for . We suggest that
in this case the model is close to or at the crossing point of lines separating
three different types of phase transitions. The proposed phase diagram in the
plane is very similar to that of the equilibrium Potts model. In
addition, our simulations confirm field-theory prediction that in two
dimensions a branching-annihilating random walk model without parity
conservation belongs to the directed percolation universality class.Comment: 8 pages, figures included, accepted in Phys.Rev.
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