21,768 research outputs found
Generalized Euler-Lagrange equations for variational problems with scale derivatives
We obtain several Euler-Lagrange equations for variational functionals
defined on a set of H\"older curves. The cases when the Lagrangian contains
multiple scale derivatives, depends on a parameter, or contains higher-order
scale derivatives are considered.Comment: Submitted on 03-Aug-2009; accepted for publication 16-March-2010; in
"Letters in Mathematical Physics"
Spin-glass behaviour on random lattices
The ground-state phase diagram of an Ising spin-glass model on a random graph
with an arbitrary fraction of ferromagnetic interactions is analysed in the
presence of an external field. Using the replica method, and performing an
analysis of stability of the replica-symmetric solution, it is shown that
, correponding to an unbiased spin glass, is a singular point in the
phase diagram, separating a region with a spin-glass phase () from a
region with spin-glass, ferromagnetic, mixed, and paramagnetic phases
()
Replica-symmetric solutions of a dilute Ising ferromagnet in a random field
We use the replica method in order to obtain an expression for the
variational free energy of an Ising ferromagnet on a Viana-Bray lattice in the
presence of random external fields. Introducing a global order parameter, in
the replica-symmetric context, the problem is reduced to the analysis of the
solutions of a nonlinear integral equation. At zero temperature, and under some
restrictions on the form of the random fields, we are able to perform a
detailed analysis of stability of the replica-symmetric solutions. In contrast
to the behaviour of the Sherrington-Kirkpatrick model for a spin glass in a
uniform field, the paramagnetic solution is fully stable in a sufficiently
large random field
Diluted antiferromagnet in a ferromagnetic enviroment
The question of robustness of a network under random ``attacks'' is treated
in the framework of critical phenomena. The persistence of spontaneous
magnetization of a ferromagnetic system to the random inclusion of
antiferromagnetic interactions is investigated. After examing the static
properties of the quenched version (in respect to the random antiferromagnetic
interactions) of the model, the persistence of the magnetization is analysed
also in the annealed approximation, and the difference in the results are
discussed
Temperature effect on (2+1) experimental Kardar-Parisi-Zhang growth
We report on the effect of substrate temperature (T) on both local structure
and long-wavelength fluctuations of polycrystalline CdTe thin films deposited
on Si(001). A strong T-dependent mound evolution is observed and explained in
terms of the energy barrier to inter-grain diffusion at grain boundaries, as
corroborated by Monte Carlo simulations. This leads to transitions from
uncorrelated growth to a crossover from random-to-correlated growth and
transient anomalous scaling as T increases. Due to these finite-time effects,
we were not able to determine the universality class of the system through the
critical exponents. Nevertheless, we demonstrate that this can be circumvented
by analyzing height, roughness and maximal height distributions, which allow us
to prove that CdTe grows asymptotically according to the Kardar-Parisi-Zhang
(KPZ) equation in a broad range of T. More important, one finds positive
(negative) velocity excess in the growth at low (high) T, indicating that it is
possible to control the KPZ non-linearity by adjusting the temperature.Comment: 6 pages, 5 figure
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