14,178 research outputs found
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
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.
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
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
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.
Broad relaxation spectrum and the field theory of glassy dynamics for pinned elastic systems
We study thermally activated, low temperature equilibrium dynamics of elastic
systems pinned by disorder using one loop functional renormalization group
(FRG). Through a series of increasingly complete approximations, we investigate
how the field theory reveals the glassy nature of the dynamics, in particular
divergent barriers and barrier distributions controling the spectrum of
relaxation times. A naive single relaxation time approximation for each
wavevector is found to be unsatisfactory. A second approximation based on a
random friction model, yields a size (L) dependent log-normal distribution of
relaxation times (mean barriers ~L^\theta and variance ~ L^{\theta/2}) and a
procedure to estimate dynamical scaling functions. Finally, we study the full
structure of the running dynamical effective action within the field theory. We
find that relaxation time distributions are non-trivial (broad but not
log-normal) and encoded in a closed hierarchy of FRG equations. A thermal
boundary layer ansatz (TBLA) appears as a consistent solution. It extends the
one discovered in the statics which was shown to embody droplet thermal
fluctuations. Although perturbative control remains a challenge, the structure
of the dynamical TBLA which encodes barrier distributions opens the way for
deeper understanding of the field theory approach to glasses
Critical Exponents for Diluted Resistor Networks
An approach by Stephen is used to investigate the critical properties of
randomly diluted resistor networks near the percolation threshold by means of
renormalized field theory. We reformulate an existing field theory by Harris
and Lubensky. By a decomposition of the principal Feynman diagrams we obtain a
type of diagrams which again can be interpreted as resistor networks. This new
interpretation provides for an alternative way of evaluating the Feynman
diagrams for random resistor networks. We calculate the resistance crossover
exponent up to second order in , where is the spatial
dimension. Our result verifies a
previous calculation by Lubensky and Wang, which itself was based on the
Potts--model formulation of the random resistor network.Comment: 27 pages, 14 figure
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