14,480 research outputs found
Microscopic Non-Universality versus Macroscopic Universality in Algorithms for Critical Dynamics
We study relaxation processes in spin systems near criticality after a quench
from a high-temperature initial state. Special attention is paid to the stage
where universal behavior, with increasing order parameter emerges from an early
non-universal period. We compare various algorithms, lattice types, and
updating schemes and find in each case the same universal behavior at
macroscopic times, despite of surprising differences during the early
non-universal stages.Comment: 9 pages, 3 figures, RevTeX, submitted to Phys. Rev. Let
Dynamic SU(2) Lattice Gauge Theory at Finite Temperature
The dynamic relaxation process for the (2+1)--dimensional SU(2) lattice gauge
theory at critical temperature is investigated with Monte Carlo methods. The
critical initial increase of the Polyakov loop is observed. The dynamic
exponents and as well as the static critical exponent
are determined from the power law behaviour of the Polyakov loop, the
auto-correlation and the second moment at the early stage of the time
evolution. The results are well consistent and universal short-time scaling
behaviour of the dynamic system is confirmed. The values of the exponents show
that the dynamic SU(2) lattice gauge theory is in the same dynamic universality
class as the dynamic Ising model.Comment: 10 pages with 2 figure
Correlated Initial Conditions in Directed Percolation
We investigate the influence of correlated initial conditions on the temporal
evolution of a (d+1)-dimensional critical directed percolation process.
Generating initial states with correlations ~r^(sigma-d) we
observe that the density of active sites in Monte-Carlo simulations evolves as
rho(t)~t^kappa. The exponent kappa depends continuously on sigma and varies in
the range -beta/nu_{||}<=kappa<=eta. Our numerical results are confirmed by an
exact field-theoretical renormalization group calculation.Comment: 10 pages, RevTeX, including 5 encapsulated postscript figure
Disordered Electrons in a Strong Magnetic Field: Transfer Matrix Approaches to the Statistics of the Local Density of States
We present two novel approaches to establish the local density of states as
an order parameter field for the Anderson transition problem. We first
demonstrate for 2D quantum Hall systems the validity of conformal scaling
relations which are characteristic of order parameter fields. Second we show
the equivalence between the critical statistics of eigenvectors of the
Hamiltonian and of the transfer matrix, respectively. Based on this equivalence
we obtain the order parameter exponent for 3D quantum
Hall systems.Comment: 4 pages, 3 Postscript figures, corrected scale in Fig.
Dynamic behavior of anisotropic non-equilibrium driving lattice gases
It is shown that intrinsically anisotropic non-equilibrium systems relaxing
by a dynamic process exhibit universal critical behavior during their evolution
toward non-equilibrium stationary states. An anisotropic scaling anzats for the
dynamics is proposed and tested numerically. Relevant critical exponents can be
evaluated self-consistently using both the short- and long-time dynamics
frameworks. The obtained results allow us to clarify a long-standing
controversy about the theoretical description, the universality and the origin
of the anisotropy of driven diffusive systems, showing that the standard field
theory does not hold and supporting a recently proposed alternative theory.Comment: 4 pages, 2 figure
Generalized Dynamic Scaling for Critical Relaxations
The dynamic relaxation process for the two dimensional Potts model at
criticality starting from an initial state with very high temperature and
arbitrary magnetization is investigated with Monte Carlo methods. The results
show that there exists universal scaling behaviour even in the short-time
regime of the dynamic evolution. In order to describe the dependence of the
scaling behaviour on the initial magnetization, a critical characteristic
function is introduced.Comment: Latex, 8 pages, 3 figures, to appear in Phys. Rev. Let
Transport on Directed Percolation Clusters
We study random lattice networks consisting of resistor like and diode like
bonds. For investigating the transport properties of these random resistor
diode networks we introduce a field theoretic Hamiltonian amenable to
renormalization group analysis. We focus on the average two-port resistance at
the transition from the nonpercolating to the directed percolating phase and
calculate the corresponding resistance exponent to two-loop order.
Moreover, we determine the backbone dimension of directed percolation
clusters to two-loop order. We obtain a scaling relation for that is in
agreement with well known scaling arguments.Comment: 4 page
One pot ‘click’ reactions: tandem enantioselective biocatalytic epoxide ring opening and [3+2] azide alkyne cycloaddition
Halohydrin dehalogenase (HheC) can perform enantioselective azidolysis of aromatic epoxides to 1,2-azido alcohols which are subsequently ligated to alkynes producing chiral hydroxy triazoles in a one-pot procedure with excellent enantiomeric excess.
Multifractal properties of resistor diode percolation
Focusing on multifractal properties we investigate electric transport on
random resistor diode networks at the phase transition between the
non-percolating and the directed percolating phase. Building on first
principles such as symmetries and relevance we derive a field theoretic
Hamiltonian. Based on this Hamiltonian we determine the multifractal moments of
the current distribution that are governed by a family of critical exponents
. We calculate the family to two-loop order in a
diagrammatic perturbation calculation augmented by renormalization group
methods.Comment: 21 pages, 5 figures, to appear in Phys. Rev.
Global Persistence in Directed Percolation
We consider a directed percolation process at its critical point. The
probability that the deviation of the global order parameter with respect to
its average has not changed its sign between 0 and t decays with t as a power
law. In space dimensions d<4 the global persistence exponent theta_p that
characterizes this decay is theta_p=2 while for d<4 its value is increased to
first order in epsilon = 4-d. Combining a method developed by Majumdar and Sire
with renormalization group techniques we compute the correction to theta_p to
first order in epsilon. The global persistence exponent is found to be a new
and independent exponent. We finally compare our results with existing
simulations.Comment: 15 pages, LaTeX, one .eps figure include
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