69 research outputs found
On the Thermodynamic Limit in Random Resistors Networks
We study a random resistors network model on a euclidean geometry \bt{Z}^d.
We formulate the model in terms of a variational principle and show that, under
appropriate boundary conditions, the thermodynamic limit of the dissipation per
unit volume is finite almost surely and in the mean. Moreover, we show that for
a particular thermodynamic limit the result is also independent of the boundary
conditions.Comment: 14 pages, LaTeX IOP journal preprint style file `ioplppt.sty',
revised version to appear in Journal of Physics
Percolation and Conduction in Restricted Geometries
The finite-size scaling behaviour for percolation and conduction is studied
in two-dimensional triangular-shaped random resistor networks at the
percolation threshold. The numerical simulations are performed using an
efficient star-triangle algorithm. The percolation exponents, linked to the
critical behaviour at corners, are in good agreement with the conformal
results. The conductivity exponent, t', is found to be independent of the shape
of the system. Its value is very close to recent estimates for the surface and
bulk conductivity exponents.Comment: 10 pages, 7 figures, TeX, IOP macros include
Separation of the magnetic phases at the N\'{e}el point in the diluted spin-Peierls magnet CuGeO3
The impurity induced antiferromagnetic ordering of the doped spin-Peierls
magnet Cu(1-x)Mg(x)GeO(3) was studied by ESR technique. Crystals with the Mg
concentration x<4% demonstrate a coexistence of paramagnetic and
antiferromagnetic ESR modes. This coexistence indicates the separation of a
macroscopically uniform sample in the paramagnetic and antiferromagnetic
phases. In the presence of the long-range spin-Peierls order (in a sample with
x=1.71%) the volume of the antiferromagnetic phase immediately below the
N\'{e}el point T_N is much smaller than the volume of the paramagnetic phase.
In the presence of the short-range spin-Peierls order (in samples with x=2.88%,
x= 3.2%) there are comparable volumes of paramagnetic and antiferromagnetic
phases at T=T_N. The fraction of the antiferromagnetic phase increases with
lowering temperature. In the absence of the spin-Peierls dimerization (at
x=4.57%)the whole sample exhibits the transition into the antiferromagnetic
state and there is no phase separation. The phase separation is explained by
the consideration of clusters of staggered magnetization located near impurity
atoms. In this model the areas occupied by coherently correlated spins expand
with decreasing temperature and the percolation of the ordered area through a
macroscopic distance occurs.Comment: 7pages, 10 figure
Hopping Conductivity of a Nearly-1d Fractal: a Model for Conducting Polymers
We suggest treating a conducting network of oriented polymer chains as an
anisotropic fractal whose dimensionality D=1+\epsilon is close to one.
Percolation on such a fractal is studied within the real space renormalization
group of Migdal and Kadanoff. We find that the threshold value and all the
critical exponents are strongly nonanalytic functions of \epsilon as \epsilon
tends to zero, e.g., the critical exponent of conductivity is \epsilon^{-2}\exp
(-1-1/\epsilon). The distribution function for conductivity of finite samples
at the percolation threshold is established. It is shown that the central body
of the distribution is given by a universal scaling function and only the
low-conductivity tail of distribution remains -dependent. Variable
range hopping conductivity in the polymer network is studied: both DC
conductivity and AC conductivity in the multiple hopping regime are found to
obey a quasi-1d Mott law. The present results are consistent with electrical
properties of poorly conducting polymers.Comment: 27 pages, RevTeX, epsf, 5 .eps figures, to be published in Phys. Rev.
Variable-range hopping conductivity in the copper-oxygen chains of La_3Sr_3Ca_8Cu_24O_41
We show that the spin chain/ladder compound La_3Sr_3Ca_8Cu_24O_41 is an
insulator with hopping transport along the chains. In the temperature range 35
- 280 K, DC conductivity sigma_{DC}(T) follows Mott's law of variable-range
hopping conduction; the frequency dependence has the form sigma(\nu, T) =
\sigma_{DC}(T) + A(T)\nu^{s}, where s \approx 1. The conduction mechanism
changes from variable-range hopping to nearest-neighbor hopping around T_{c}
=300 K. The chain array thus behaves like a one-dimensional disordered system.
Disorder is due to random structural distortions of chains induced by irregular
coordination of the La/Sr/Ca ions.Comment: 4 pages, 3 figures, accepted for publication in PR
Luminescence spectra and kinetics of disordered solid solutions
We have studied both theoretically and experimentally the luminescence spectra and kinetics of crystalline, disordered solid solutions after pulsed excitation. First, we present the model calculations of the steady-state luminescence band shape caused by recombination of excitons localized in the wells of random potential induced by disorder. Classification of optically active tail states of the main exciton band into two groups is proposed. The majority of the states responsible for the optical absorption corresponds to the group of extended states belonging to the percolation cluster, whereas only a relatively small group of “radiative” states forms the steady-state luminescence band. The continuum percolation theory is applied to distinguish the “radiative” localized states, which are isolated in space and have no ways for nonradiative transitions along the tail states. It is found that the analysis of the exciton-phonon interaction gives the information about the character of the localization of excitons. We have shown that the model used describes quite well the experimental cw spectra of CdS(1−c)Sec and ZnSe(1−c)Tec solid solutions. Further, the experimental results are presented for the temporal evolution of the luminescence band. It is shown that the changes of band shape with time come from the interplay of population dynamics of extended states and spatially isolated “radiative” states. Finally, the measurements of the decay of the spectrally integrated luminescence intensity at long delay times are presented. It is shown that the observed temporal behavior can be described in terms of relaxation of separated pairs followed by subsequent exciton formation and radiative recombination. Electron tunneling processes are supposed to be responsible for the luminescence in the long-time limit at excitation below the exciton mobility edge. At excitation by photons with higher energies the diffusion of electrons can account for the observed behavior of the luminescence
Percolation and cluster distribution. III. Algorithms for the site-bond problem
Algorithms for estimating the percolation probabilities and cluster size distribution are given in the framework of a Monte Carlo simulation for disordered lattices for the generalized site-bond problem. The site-bond approach is useful when a percolation process cannot be exclusively described in the context of pure site or pure bond percolation. An extended multiple labeling technique (ECMLT) is introduced for the generalized problem. The ECMLT is applied to the site-bond percolation problem for square and triangular lattices. Numerical data are given for lattices containing up to 16 million sites. An application to polymer gelation is suggested.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45140/1/10955_2005_Article_BF01011170.pd
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