261 research outputs found
On isoperimetric inequalities with respect to infinite measures
We study isoperimetric problems with respect to infinite measures on .
In the case of the measure defined by , ,
we prove that, among all sets with given measure, the ball centered at
the origin has the smallest (weighted) perimeter. Our results are then
applied to obtain Polya-Szego-type inequalities, Sobolev embeddings theorems
and a comparison result for elliptic boundary value problems.Comment: 25 page
Microwave Electrodynamics of the Antiferromagnetic Superconductor GdBa_2Cu_3O_{7-\delta}
The temperature dependence of the microwave surface impedance and
conductivity are used to study the pairing symmetry and properties of cuprate
superconductors. However, the superconducting properties can be hidden by the
effects of paramagnetism and antiferromagnetic long-range order in the
cuprates. To address this issue we have investigated the microwave
electrodynamics of GdBa_2Cu_3O_{7-\delta}, a rare-earth cuprate superconductor
which shows long-range ordered antiferromagnetism below T_N=2.2 K, the Neel
temperature of the Gd ion subsystem. We measured the temperature dependence of
the surface resistance and surface reactance of c-axis oriented epitaxial thin
films at 10.4, 14.7 and 17.9 GHz with the parallel plate resonator technique
down to 1.4 K. Both the resistance and the reactance data show an unusual
upturn at low temperature and the resistance presents a strong peak around T_N
mainly due to change in magnetic permeability.Comment: M2S-HTCS-VI Conference Paper, 2 pages, 2 eps figures, using Elsevier
style espcrc2.st
Critical and tricritical singularities of the three-dimensional random-bond Potts model for large
We study the effect of varying strength, , of bond randomness on the
phase transition of the three-dimensional Potts model for large . The
cooperative behavior of the system is determined by large correlated domains in
which the spins points into the same direction. These domains have a finite
extent in the disordered phase. In the ordered phase there is a percolating
cluster of correlated spins. For a sufficiently large disorder
this percolating cluster coexists with a percolating cluster
of non-correlated spins. Such a co-existence is only possible in more than two
dimensions. We argue and check numerically that is the tricritical
disorder, which separates the first- and second-order transition regimes. The
tricritical exponents are estimated as and
. We claim these exponents are independent, for sufficiently
large . In the second-order transition regime the critical exponents
and are independent of the strength of
disorder.Comment: 12 pages, 11 figure
Finsler Hardy inequalities
In this paper we present a unified simple approach to anisotropic Hardy
inequalities in various settings. We consider Hardy inequalities which involve
a Finsler distance from a point or from the boundary of a domain. The sharpness
and the non-attainability of the constants in the inequalities are also proved.Comment: 31 pages. We add "Note added to Proof" in Introduction and several
reference
Quantum tricriticality in transverse Ising-like systems
The quantum tricriticality of d-dimensional transverse Ising-like systems is
studied by means of a perturbative renormalization group approach focusing on
static susceptibility. This allows us to obtain the phase diagram for 3<d<4,
with a clear location of the critical lines ending in the conventional quantum
critical points and in the quantum tricritical one, and of the tricritical line
for temperature T \geq 0. We determine also the critical and the tricritical
shift exponents close to the corresponding ground state instabilities.
Remarkably, we find a tricritical shift exponent identical to that found in the
conventional quantum criticality and, by approaching the quantum tricritical
point increasing the non-thermal control parameter r, a crossover of the
quantum critical shift exponents from the conventional value \phi = 1/(d-1) to
the new one \phi = 1/2(d-1). Besides, the projection in the (r,T)-plane of the
phase boundary ending in the quantum tricritical point and crossovers in the
quantum tricritical region appear quite similar to those found close to an
usual quantum critical point. Another feature of experimental interest is that
the amplitude of the Wilsonian classical critical region around this peculiar
critical line is sensibly smaller than that expected in the quantum critical
scenario. This suggests that the quantum tricriticality is essentially governed
by mean-field critical exponents, renormalized by the shift exponent \phi =
1/2(d-1) in the quantum tricritical region.Comment: 9 pages, 2 figures; to be published on EPJ
Transport Anomalies and Marginal Fermi-Liquid Effects at a Quantum Critical Point
The behavior of the conductivity and the density of states, as well as the
phase relaxation time, of disordered itinerant electrons across a quantum
ferromagnetic transition is discussed. It is shown that critical fluctuations
lead to anomalies in the temperature and energy dependence of the conductivity
and the tunneling density of states, respectively, that are stronger than the
usual weak-localization anomalies in a disordered Fermi liquid. This can be
used as an experimental probe of the quantum critical behavior. The energy
dependence of the phase relaxation time at criticality is shown to be that of a
marginal Fermi liquid.Comment: 4 pp., LaTeX, no figs., requires World Scientific style files
(included), Contribution to MB1
Uniqueness of renormalized solutions to nonlinear elliptic equations with a lower order term and right-hand side in
Disorder induced rounding of the phase transition in the large q-state Potts model
The phase transition in the q-state Potts model with homogeneous
ferromagnetic couplings is strongly first order for large q, while is rounded
in the presence of quenched disorder. Here we study this phenomenon on
different two-dimensional lattices by using the fact that the partition
function of the model is dominated by a single diagram of the high-temperature
expansion, which is calculated by an efficient combinatorial optimization
algorithm. For a given finite sample with discrete randomness the free energy
is a pice-wise linear function of the temperature, which is rounded after
averaging, however the discontinuity of the internal energy at the transition
point (i.e. the latent heat) stays finite even in the thermodynamic limit. For
a continuous disorder, instead, the latent heat vanishes. At the phase
transition point the dominant diagram percolates and the total magnetic moment
is related to the size of the percolating cluster. Its fractal dimension is
found d_f=(5+\sqrt{5})/4 and it is independent of the type of the lattice and
the form of disorder. We argue that the critical behavior is exclusively
determined by disorder and the corresponding fixed point is the isotropic
version of the so called infinite randomness fixed point, which is realized in
random quantum spin chains. From this mapping we conjecture the values of the
critical exponents as \beta=2-d_f, \beta_s=1/2 and \nu=1.Comment: 12 pages, 12 figures, version as publishe
Interface mapping in two-dimensional random lattice models
We consider two disordered lattice models on the square lattice: on the
medial lattice the random field Ising model at T=0 and on the direct lattice
the random bond Potts model in the large-q limit at its transition point. The
interface properties of the two models are known to be related by a mapping
which is valid in the continuum approximation. Here we consider finite random
samples with the same form of disorder for both models and calculate the
respective equilibrium states exactly by combinatorial optimization algorithms.
We study the evolution of the interfaces with the strength of disorder and
analyse and compare the interfaces of the two models in finite lattices.Comment: 7 pages, 6 figure
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