342 research outputs found
Scaling properties in off equilibrium dynamical processes
In the present paper, we analyze the consequences of scaling hypotheses on
dynamic functions, as two times correlations . We show, under general
conditions, that must obey the following scaling behavior , where the scaling variable is
and , two
undetermined functions. The presence of a non constant exponent
signals the appearance of multiscaling properties in the dynamics.Comment: 6 pages, no figure
Persistence of a particle in the Matheron-de Marsily velocity field
We show that the longitudinal position of a particle in a
-dimensional layered random velocity field (the Matheron-de Marsily
model) can be identified as a fractional Brownian motion (fBm) characterized by
a variable Hurst exponent for . The
fBm becomes marginal at . Moreover, using the known first-passage
properties of fBm we prove analytically that the disorder averaged persistence
(the probability of no zero crossing of the process upto time ) has a
power law decay for large with an exponent for and
for (with logarithmic correction at ), results that
were earlier derived by Redner based on heuristic arguments and supported by
numerical simulations (S. Redner, Phys. Rev. E {\bf 56}, 4967 (1997)).Comment: 4 pages Revtex, 1 .eps figure included, to appear in PRE Rapid
Communicatio
Dimer coverings on the Sierpinski gasket with possible vacancies on the outmost vertices
We present the number of dimers on the Sierpinski gasket
at stage with dimension equal to two, three, four or five, where one of
the outmost vertices is not covered when the number of vertices is an
odd number. The entropy of absorption of diatomic molecules per site, defined
as , is calculated to be
exactly for . The numbers of dimers on the generalized
Sierpinski gasket with and are also obtained
exactly. Their entropies are equal to , , ,
respectively. The upper and lower bounds for the entropy are derived in terms
of the results at a certain stage for with . As the
difference between these bounds converges quickly to zero as the calculated
stage increases, the numerical value of with can be
evaluated with more than a hundred significant figures accurate.Comment: 35 pages, 20 figures and 1 tabl
Field-induced XY behavior in the S=1/2 antiferromagnet on the square lattice
Making use of the quantum Monte Carlo method based on the worm algorithm, we
study the thermodynamic behavior of the S=1/2 isotropic Heisenberg
antiferromagnet on the square lattice in a uniform magnetic field varying from
very small values up to the saturation value. The field is found to induce a
Berezinskii-Kosterlitz-Thouless transition at a finite temperature, above which
a genuine XY behavior in an extended temperature range is observed. The phase
diagram of the system is drawn, and the thermodynamic behavior of the specific
heat and of the uniform and staggered magnetization is discussed in sight of an
experimental investigation of the field-induced XY behavior.Comment: 4 pages, 4 figure
Thermodynamics of Random Ferromagnetic Antiferromagnetic Spin-1/2 Chains
Using the quantum Monte Carlo Loop algorithm, we calculate the temperature
dependence of the uniform susceptibility, the specific heat, the correlation
length, the generalized staggered susceptibility and magnetization of a
spin-1/2 chain with random antiferromagnetic and ferromagnetic couplings, down
to very low temperatures. Our data show a consistent scaling behavior in all
the quantities and support strongly the conjecture drawn from the approximate
real-space renormalization group treatment.A statistical analysis scheme is
developed which will be useful for the search of scaling behavior in numerical
and experimental data of random spin chains.Comment: 13 pages, 13 figures, RevTe
Noisy random resistor networks: renormalized field theory for the multifractal moments of the current distribution
We study the multifractal moments of the current distribution in randomly
diluted resistor networks near the percolation treshold. When an external
current is applied between to terminals and of the network, the
th multifractal moment scales as , where is the correlation length exponent of
the isotropic percolation universality class. By applying our concept of master
operators [Europhys. Lett. {\bf 51}, 539 (2000)] we calculate the family of
multifractal exponents for to two-loop order. We find
that our result is in good agreement with numerical data for three dimensions.Comment: 30 pages, 6 figure
Quantum Monte Carlo with Directed Loops
We introduce the concept of directed loops in stochastic series expansion and
path integral quantum Monte Carlo methods. Using the detailed balance rules for
directed loops, we show that it is possible to smoothly connect generally
applicable simulation schemes (in which it is necessary to include
back-tracking processes in the loop construction) to more restricted loop
algorithms that can be constructed only for a limited range of Hamiltonians
(where back-tracking can be avoided). The "algorithmic discontinuities" between
general and special points (or regions) in parameter space can hence be
eliminated. As a specific example, we consider the anisotropic S=1/2 Heisenberg
antiferromagnet in an external magnetic field. We show that directed loop
simulations are very efficient for the full range of magnetic fields (zero to
the saturation point) and anisotropies. In particular for weak fields and
anisotropies, the autocorrelations are significantly reduced relative to those
of previous approaches. The back-tracking probability vanishes continuously as
the isotropic Heisenberg point is approached. For the XY-model, we show that
back-tracking can be avoided for all fields extending up to the saturation
field. The method is hence particularly efficient in this case. We use directed
loop simulations to study the magnetization process in the 2D Heisenberg model
at very low temperatures. For LxL lattices with L up to 64, we utilize the
step-structure in the magnetization curve to extract gaps between different
spin sectors. Finite-size scaling of the gaps gives an accurate estimate of the
transverse susceptibility in the thermodynamic limit: chi_perp = 0.0659 +-
0.0002.Comment: v2: Revised and expanded discussion of detailed balance, error in
algorithmic phase diagram corrected, to appear in Phys. Rev.
Monte Carlo Methods for Estimating Interfacial Free Energies and Line Tensions
Excess contributions to the free energy due to interfaces occur for many
problems encountered in the statistical physics of condensed matter when
coexistence between different phases is possible (e.g. wetting phenomena,
nucleation, crystal growth, etc.). This article reviews two methods to estimate
both interfacial free energies and line tensions by Monte Carlo simulations of
simple models, (e.g. the Ising model, a symmetrical binary Lennard-Jones fluid
exhibiting a miscibility gap, and a simple Lennard-Jones fluid). One method is
based on thermodynamic integration. This method is useful to study flat and
inclined interfaces for Ising lattices, allowing also the estimation of line
tensions of three-phase contact lines, when the interfaces meet walls (where
"surface fields" may act). A generalization to off-lattice systems is described
as well.
The second method is based on the sampling of the order parameter
distribution of the system throughout the two-phase coexistence region of the
model. Both the interface free energies of flat interfaces and of (spherical or
cylindrical) droplets (or bubbles) can be estimated, including also systems
with walls, where sphere-cap shaped wall-attached droplets occur. The
curvature-dependence of the interfacial free energy is discussed, and estimates
for the line tensions are compared to results from the thermodynamic
integration method. Basic limitations of all these methods are critically
discussed, and an outlook on other approaches is given
Consequences of temperature fluctuations in observables measured in high energy collisions
We review the consequences of intrinsic, nonstatistical temperature
fluctuations as seen in observables measured in high energy collisions. We do
this from the point of view of nonextensive statistics and Tsallis
distributions. Particular attention is paid to multiplicity fluctuations as a
first consequence of temperature fluctuations, to the equivalence of
temperature and volume fluctuations, to the generalized thermodynamic
fluctuations relations allowing us to compare fluctuations observed in
different parts of phase space, and to the problem of the relation between
Tsallis entropy and Tsallis distributions. We also discuss the possible
influence of conservation laws on these distributions and provide some examples
of how one can get them without considering temperature fluctuations.Comment: Revised version of the invited contribution to The European Physical
Journal A (Hadrons and Nuclei) topical issue about 'Relativistic Hydro- and
Thermodynamics in Nuclear Physics' guest eds. Tamas S. Biro, Gergely G.
Barnafoldi and Peter Va
Statistical Outliers and Dragon-Kings as Bose-Condensed Droplets
A theory of exceptional extreme events, characterized by their abnormal sizes
compared with the rest of the distribution, is presented. Such outliers, called
"dragon-kings", have been reported in the distribution of financial drawdowns,
city-size distributions (e.g., Paris in France and London in the UK), in
material failure, epileptic seizure intensities, and other systems. Within our
theory, the large outliers are interpreted as droplets of Bose-Einstein
condensate: the appearance of outliers is a natural consequence of the
occurrence of Bose-Einstein condensation controlled by the relative degree of
attraction, or utility, of the largest entities. For large populations, Zipf's
law is recovered (except for the dragon-king outliers). The theory thus
provides a parsimonious description of the possible coexistence of a power law
distribution of event sizes (Zipf's law) and dragon-king outliers.Comment: Latex file, 16 pages, 1 figur
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