211 research outputs found
Direct Evidence of the Discontinuous Character of the Kosterlitz-Thouless Jump
It is numerically shown that the discontinuous character of the helicity
modulus of the two-dimensional XY model at the Kosterlitz-Thouless (KT)
transition can be directly related to a higher order derivative of the free
energy without presuming any {\it a priori} knowledge of the nature of the
transition. It is also suggested that this higher order derivative is of
intrinsic interest in that it gives an additional characteristics of the KT
transition which might be associated with a universal number akin to the
universal value of the helicity modulus at the critical temperature.Comment: 4 pages, to appear in PR
Resistance scaling at the Kosterlitz-Thouless transition
We study the linear resistance at the Kosterlitz-Thouless transition by Monte
Carlo simulation of vortex dynamics. Finite size scaling analysis of our data
show excellent agreement with scaling properties of the Kosterlitz-Thouless
transition. We also compare our results for the linear resistance with
experiments. By adjusting the vortex chemical potential to an optimum value,
the resistance at temperatures above the transition temperature agrees well
with experiments over many decades.Comment: 7 pages, 4 postscript figures included, LATEX, KTH-CMT-94-00
Neutral theory of chemical reaction networks
To what extent do the characteristic features of a chemical reaction network
reflect its purpose and function? In general, one argues that correlations
between specific features and specific functions are key to understanding a
complex structure. However, specific features may sometimes be neutral and
uncorrelated with any system-specific purpose, function or causal chain. Such
neutral features are caused by chance and randomness. Here we compare two
classes of chemical networks: one that has been subjected to biological
evolution (the chemical reaction network of metabolism in living cells) and one
that has not (the atmospheric planetary chemical reaction networks). Their
degree distributions are shown to share the very same neutral
system-independent features. The shape of the broad distributions is to a large
extent controlled by a single parameter, the network size. From this
perspective, there is little difference between atmospheric and metabolic
networks; they are just different sizes of the same random assembling network.
In other words, the shape of the degree distribution is a neutral
characteristic feature and has no functional or evolutionary implications in
itself; it is not a matter of life and death.Comment: 13 pages, 8 figure
The Blind Watchmaker Network: Scale-freeness and Evolution
It is suggested that the degree distribution for networks of the
cell-metabolism for simple organisms reflects an ubiquitous randomness. This
implies that natural selection has exerted no or very little pressure on the
network degree distribution during evolution. The corresponding random network,
here termed the blind watchmaker network has a power-law degree distribution
with an exponent gamma >= 2. It is random with respect to a complete set of
network states characterized by a description of which links are attached to a
node as well as a time-ordering of these links. No a priory assumption of any
growth mechanism or evolution process is made. It is found that the degree
distribution of the blind watchmaker network agrees very precisely with that of
the metabolic networks. This implies that the evolutionary pathway of the
cell-metabolism, when projected onto a metabolic network representation, has
remained statistically random with respect to a complete set of network states.
This suggests that even a biological system, which due to natural selection has
developed an enormous specificity like the cellular metabolism, nevertheless
can, at the same time, display well defined characteristics emanating from the
ubiquitous inherent random element of Darwinian evolution. The fact that also
completely random networks may have scale-free node distributions gives a new
perspective on the origin of scale-free networks in general.Comment: 5 pages, 3 figure
Hierarchy Measures in Complex Networks
Using each node's degree as a proxy for its importance, the topological
hierarchy of a complex network is introduced and quantified. We propose a
simple dynamical process used to construct networks which are either maximally
or minimally hierarchical. Comparison with these extremal cases as well as with
random scale-free networks allows us to better understand hierarchical versus
modular features in several real-life complex networks. For random scale-free
topologies the extent of topological hierarchy is shown to smoothly decline
with -- the exponent of a degree distribution -- reaching its highest
possible value for and quickly approaching zero for .Comment: 4 pages, 4 figure
Vortex Fluctuations in High-Tc Films: Flux Noise Spectrum and Complex Impedance
The flux noise spectrum and complex impedance for a 500 {\AA} thick YBCO film
are measured and compared with predictions for two dimensional vortex
fluctuations. It is verified that the complex impedance and the flux noise
spectra are proportional to each other, that the logarithm of the flux noise
spectra for different temperatures has a common tangent with slope , and that the amplitude of the noise decreases as , where is
the height above the film at which the magnetic flux is measured. A crossover
from normal to anomalous vortex diffusion is indicated by the measurements and
is discussed in terms of a two-dimensional decoupling.Comment: 5 pages including 4 figures in two columns, to appear in Phys. Rev.
Let
Scaling determination of the nonlinear I-V characteristics for 2D superconducting networks
It is shown from computer simulations that the current-voltage (-)
characteristics for the two-dimensional XY model with resistively-shunted
Josephson junction dynamics and Monte Carlo dynamics obeys a finite-size
scaling form from which the nonlinear - exponent can be determined to
good precision. This determination supports the conclusion , where
is the dynamic critical exponent. The results are discussed in the light of the
contrary conclusion reached by Tang and Chen [Phys. Rev. B {\bf 67}, 024508
(2003)] and the possibility of a breakdown of scaling suggested by Bormann
[Phys. Rev. Lett. {\bf 78}, 4324 (1997)].Comment: 6 pages, to appear in PR
Possible first order transition in the two-dimensional Ginzburg-Landau model induced by thermally fluctuating vortex cores
We study the two-dimensional Ginzburg-Landau model of a neutral superfluid in
the vicinity of the vortex unbinding transition. The model is mapped onto an
effective interacting vortex gas by a systematic perturbative elimination of
all fluctuating degrees of freedom (amplitude {\em and} phase of the order
parameter field) except the vortex positions. In the Coulomb gas descriptions
derived previously in the literature, thermal amplitude fluctuations were
neglected altogether. We argue that, if one includes the latter, the vortices
still form a two- dimensional Coulomb gas, but the vortex fugacity can be
substantially raised. Under the assumption that Minnhagen's generic phase
diagram of the two- dimensional Coulomb gas is correct, our results then point
to a first order transition rather than a Kosterlitz-Thouless transition,
provided the Ginzburg-Landau correlation length is large enough in units of a
microscopic cutoff length for fluctuations. The experimental relevance of these
results is briefly discussed. [Submitted to J. Stat. Phys.]Comment: 36 pages, LaTeX, 6 figures upon request, UATP2-DB1-9
Evidence of Two Distinct Dynamic Critical Exponents in Connection with Vortex Physics
The dynamic critical exponent is determined from numerical simulations
for the three-dimensional (3D) lattice Coulomb gas (LCG) and the 3D XY models
with relaxational dynamics. It is suggested that the dynamics is characterized
by two distinct dynamic critical indices and related to the
divergence of the relaxation time by and
, where is the correlation length and the
wavevector. The values determined are and for the
3D LCG and and for the 3D XY model. It is argued
that the nonlinear exponent relates to , whereas the usual
Hohenberg-Halperin classification relates to . Possible implications for the
interpretation of experiments are pointed out. Comparisons with other existing
results are discussed.Comment: to appear in PR
Systematic vertex corrections through iterative solution of Hedin's equations beyond the it GW approximation
We present a general procedure for obtaining progressively more accurate functional expressions for the electron self-energy by iterative solution of Hedin's coupled equations. The iterative process starting from Hartree theory, which gives rise to the GW approximation, is continued further, and an explicit formula for the vertex function from the second full cycle is given. Calculated excitation energies for a Hubbard Hamiltonian demonstrate the convergence of the iterative process and provide further strong justification for the GW approximation
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