1,407 research outputs found
Critical Behavior of the Ferromagnetic Ising Model on a Sierpinski Carpet: Monte Carlo Renormalization Group Study
We perform a Monte Carlo Renormalization Group analysis of the critical
behavior of the ferromagnetic Ising model on a Sierpi\'nski fractal with
Hausdorff dimension . This method is shown to be relevant to
the calculation of the critical temperature and the magnetic
eigen-exponent on such structures. On the other hand, scaling corrections
hinder the calculation of the temperature eigen-exponent . At last, the
results are shown to be consistent with a finite size scaling analysis.Comment: 16 pages, 7 figure
Towards a dephasing diode: asymmetric and geometric dephasing
We study the effect of a noisy environment on spin and charge transport in
ballistic quantum wires with spin-orbit coupling (Rashba coupling). We find
that the wire then acts as a ``dephasing diode'', inducing very different
dephasing of the spins of right and left movers. We also show how Berry phase
(geometric phase) in a curved wire can induce such asymmetric dephasing, in
addition to purely geometric dephasing. We propose ways to measure these
effects through spin detectors, spin-echo techniques, and Aharanov-Bohm
interferometry.Comment: 4 pages (2 fig) v2: extensive improvements to "readability" &
references adde
Scaling law of Wolff cluster surface energy
We study the scaling properties of the clusters grown by the Wolff algorithm
on seven different Sierpinski-type fractals of Hausdorff dimension in the framework of the Ising model. The mean absolute value of the surface
energy of Wolff cluster follows a power law with respect to the lattice size.
Moreover, we investigate the probability density distribution of the surface
energy of Wolff cluster and are able to establish a new scaling relation. It
enables us to introduce a new exponent associated to the surface energy of
Wolff cluster. Finally, this new exponent is linked to a dynamical exponent via
an inequality.Comment: 12 pages, 3 figures. To appear in PR
Critical behavior of the 3-state Potts model on Sierpinski carpet
We study the critical behavior of the 3-state Potts model, where the spins
are located at the centers of the occupied squares of the deterministic
Sierpinski carpet. A finite-size scaling analysis is performed from Monte Carlo
simulations, for a Hausdorff dimension . The phase
transition is shown to be a second order one. The maxima of the susceptibility
of the order parameter follow a power law in a very reliable way, which enables
us to calculate the ratio of the exponents . We find that the
scaling corrections affect the behavior of most of the thermodynamical
quantities. However, the sequence of intersection points extracted from the
Binder's cumulant provides bounds for the critical temperature. We are able to
give the bounds for the exponent as well as for the ratio of the
exponents , which are compatible with the results calculated from
the hyperscaling relation.Comment: 13 pages, 4 figure
Metric characterization of cluster dynamics on the Sierpinski gasket
We develop and implement an algorithm for the quantitative characterization
of cluster dynamics occurring on cellular automata defined on an arbitrary
structure. As a prototype for such systems we focus on the Ising model on a
finite Sierpsinski Gasket, which is known to possess a complex thermodynamic
behavior. Our algorithm requires the projection of evolving configurations into
an appropriate partition space, where an information-based metrics (Rohlin
distance) can be naturally defined and worked out in order to detect the
changing and the stable components of clusters. The analysis highlights the
existence of different temperature regimes according to the size and the rate
of change of clusters. Such regimes are, in turn, related to the correlation
length and the emerging "critical" fluctuations, in agreement with previous
thermodynamic analysis, hence providing a non-trivial geometric description of
the peculiar critical-like behavior exhibited by the system. Moreover, at high
temperatures, we highlight the existence of different time scales controlling
the evolution towards chaos.Comment: 20 pages, 8 figure
Incoherent scatterer in a Luttinger liquid: a new paradigmatic limit
We address the problem of a Luttinger liquid with a scatterer that allows for
both coherent and incoherent scattering channels. The asymptotic behavior at
zero temperature is governed by a new stable fixed point: a Goldstone mode
dominates the low energy dynamics, leading to a universal behavior. This limit
is marked by equal probabilities for forward and backward scattering.
Notwithstanding this non-trivial scattering pattern, we find that the shot
noise as well as zero cross-current correlations vanish. We thus present a
paradigmatic picture of an impurity in the Luttinger model, alternative to the
Kane-Fisher picture.Comment: published version, 4 + epsilon pages, 1 figur
Spontaneous magnetization of the Ising model on the Sierpinski carpet fractal, a rigorous result
We give a rigorous proof of the existence of spontaneous magnetization at
finite temperature for the Ising spin model defined on the Sierpinski carpet
fractal. The theorem is inspired by the classical Peierls argument for the two
dimensional lattice. Therefore, this exact result proves the existence of
spontaneous magnetization for the Ising model in low dimensional structures,
i.e. structures with dimension smaller than 2.Comment: 14 pages, 8 figure
Entanglement entropy and quantum phase transitions in quantum dots coupled to Luttinger liquid wires
We study a quantum phase transition which occurs in a system composed of two
impurities (or quantum dots) each coupled to a different interacting
(Luttinger-liquid) lead. While the impurities are coupled electrostatically,
there is no tunneling between them. Using a mapping of this system onto a Kondo
model, we show analytically that the system undergoes a
Berezinskii-Kosterlitz-Thouless quantum phase transition as function of the
Luttinger liquid parameter in the leads and the dot-lead interaction. The phase
with low values of the Luttinger-liquid parameter is characterized by an abrupt
switch of the population between the impurities as function of a common applied
gate voltage. However, this behavior is hard to verify numerically since one
would have to study extremely long systems. Interestingly though, at the
transition the entanglement entropy drops from a finite value of to
zero. The drop becomes sharp for infinite systems. One can employ finite size
scaling to extrapolate the transition point and the behavior in its vicinity
from the behavior of the entanglement entropy in moderate size samples. We
employ the density matrix renormalization group numerical procedure to
calculate the entanglement entropy of systems with lead lengths of up to 480
sites. Using finite size scaling we extract the transition value and show it to
be in good agreement with the analytical prediction.Comment: 12 pages, 9 figure
Conductance of Aharonov--Bohm Rings: From the Discrete to the Continuous Spectrum Limit
The dissipative conductance of an array of mesoscopic rings, subject to an
a.c. magnetic flux is investigated. The magneto--conductance may change sign
between canonical and grand-canonical statistical ensembles, as function of the
inelastic level broadening and as function of the temperature. Differences
between canonical and grand-canonical ensembles persist up to temperature of
the order of the Thouless energy.Comment: 13 pages, 2 figures, REVTeX v2.1, WIS--93/121/Dec.--P
Universal Conductance Distribution in the Quantum Size Regime
We study the conductance (g) distribution function of an ensemble of isolated
conducting rings, with an Aharonov--Bohm flux. This is done in the discrete
spectrum limit, i.e., when the inelastic rate, frequency and temperature are
all smaller than the mean level spacing. Over a wide range of g the
distribution function exhibits universal behavior P(g)\sim g^{-(4+\beta)/3},
where \beta=1 (2) for systems with (without) a time reversal symmetry. The
nonuniversal large g tail of this distribution determines the values of high
moments.Comment: 13 pages+1 figure, RevTEX
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