7,410 research outputs found
Scaling behavior of the energy gap of spin-1/2 AF-Heisenberg chain in both uniform and staggered fields
We have studied the energy gap of the 1D AF-Heisenberg model in the presence
of both uniform () and staggered () magnetic fields using the exact
diagonalization technique. We have found that the opening of the gap in the
presence of a staggered field scales with , where is the
critical exponent and depends on the uniform field. With respect to the range
of the staggered magnetic field, we have identified two regimes through which
the -dependence of the real critical exponent can be numerically
calculated. Our numerical results are in good agreement with the results
obtained by theoretical approaches
Directed abelian algebras and their applications to stochastic models
To each directed acyclic graph (this includes some D-dimensional lattices)
one can associate some abelian algebras that we call directed abelian algebras
(DAA). On each site of the graph one attaches a generator of the algebra. These
algebras depend on several parameters and are semisimple. Using any DAA one can
define a family of Hamiltonians which give the continuous time evolution of a
stochastic process. The calculation of the spectra and ground state
wavefunctions (stationary states probability distributions) is an easy
algebraic exercise. If one considers D-dimensional lattices and choose
Hamiltonians linear in the generators, in the finite-size scaling the
Hamiltonian spectrum is gapless with a critical dynamic exponent . One
possible application of the DAA is to sandpile models. In the paper we present
this application considering one and two dimensional lattices. In the one
dimensional case, when the DAA conserves the number of particles, the
avalanches belong to the random walker universality class (critical exponent
). We study the local densityof particles inside large
avalanches showing a depletion of particles at the source of the avalanche and
an enrichment at its end. In two dimensions we did extensive Monte-Carlo
simulations and found .Comment: 14 pages, 9 figure
From conformal invariance to quasistationary states
In a conformal invariant one-dimensional stochastic model, a certain
non-local perturbation takes the system to a new massless phase of a special
kind. The ground-state of the system is an adsorptive state. Part of the
finite-size scaling spectrum of the evolution Hamiltonian stays unchanged but
some levels go exponentially to zero for large lattice sizes becoming
degenerate with the ground-state. As a consequence one observes the appearance
of quasistationary states which have a relaxation time which grows
exponentially with the size of the system. Several initial conditions have
singled out a quasistationary state which has in the finite-size scaling limit
the same properties as the stationary state of the conformal invariant model.Comment: 20 pages, 15 figure
Preventing Advanced Persistent Threats in Complex Control Networks
An Advanced Persistent Threat (APT) is an emerging attack against Industrial Control and Automation Systems, that is executed over a long period of time and is difficult to detect. In this context, graph theory can be applied to model the interaction among nodes and the complex attacks affecting them, as well as to design recovery techniques that ensure the survivability of the network. Accordingly, we leverage a decision model to study how a set of hierarchically selected nodes can collaborate to detect an APT within the network, concerning the presence of changes in its topology. Moreover, we implement a response service based on redundant links that dynamically uses a secret sharing scheme and applies a flexible routing protocol depending on the severity of the attack. The ultimate goal is twofold: ensuring the reachability between nodes despite the changes and preventing the path followed by messages from being discovered.Universidad de Málaga. Campus de Excelencia Internacional AndalucÃa Tech
The phase diagram of the anisotropic Spin-1 Heisenberg Chain
We applied the Density Matrix Renormalization Group to the XXZ spin-1 quantum
chain. In studing this model we aim to clarify controversials about the point
where the massive Haldane phase appears.Comment: 2 pages (standart LaTex), 1 figure (PostScript) uuencode
Bethe Ansatz and boundary energy of the open spin-1/2 XXZ chain
We review recent results on the Bethe Ansatz solutions for the eigenvalues of
the transfer matrix of an integrable open XXZ quantum spin chain using
functional relations which the transfer matrix obeys at roots of unity. First,
we consider a case where at most two of the boundary parameters
{{,,,}} are nonzero. A generalization of
the Baxter equation that involves more than one independent is
described. We use this solution to compute the boundary energy of the chain in
the thermodynamic limit. We conclude the paper with a review of some results
for the general integrable boundary terms, where all six boundary parameters
are arbitrary.Comment: 6 pages, Latex; contribution to the XVth International Colloquium on
Integrable Systems and Quantum Symmetries, Prague, June 2006. To appear in
Czechoslovak Journal of Physics (2006); (v2) Typos corrected and a new line
added in the Acknowledgments sectio
Numerical evidences of spin-1/2 chain approaching spin-1 chain
In this article, we study the one dimensional Heisenberg spin-1/2 alternating
bond chain in which the nearest neighbor exchange couplings are ferromagnetic
(FM) and antiferromagnetic (AF) alternatively. By using exact diagonalization
and density matrix renormalization groups (DMRG) method, we discuss how the
system approaches to the AF uniform spin-1 chain under certain condition. When
the ratio of AF to FM coupling strength}
\textit{is very small, the physical quantities of the alternating bond chain
such as the spin-spin correlation, the string correlation function and the spin
density coincide with that of the AF uniform spin-1 chain. The edge state
problem is discussed in the present model with small}\textit{limit. In
addition, the Haldane gap of the AF uniform spin-1 chain is 4-times of the gap
of the system considered.Comment: 9pages,8page
Magnetic properties of the spin Heisenberg chain with hexamer modulation of exchange
We consider the spin-1/2 Heisenberg chain with alternating spin exchange %on
even and odd sites in the presence of additional modulation of exchange on odd
bonds with period three. We study the ground state magnetic phase diagram of
this hexamer spin chain in the limit of very strong antiferromagnetic (AF)
exchange on odd bonds using the numerical Lanczos method and bosonization
approach. In the limit of strong magnetic field commensurate with the
dominating AF exchange, the model is mapped onto an effective Heisenberg
chain in the presence of uniform and spatially modulated fields, which is
studied using the standard continuum-limit bosonization approach. In absence of
additional hexamer modulation, the model undergoes a quantum phase transition
from a gapped string order into the only one gapless L\"uttinger liquid (LL)
phase by increasing the magnetic field. In the presence of hexamer modulation,
two new gapped phases are identified in the ground state at magnetization equal
to 1/3 and 2/3 of the saturation value. These phases reveal themselves also in
magnetization curve as plateaus at corresponding values of magnetization. As
the result, the magnetic phase diagram of the hexamer chain shows seven
different quantum phases, four gapped and three gapless and the system is
characterized by six critical fields which mark quantum phase transitions
between the ordered gapped and the LL gapless phases.Comment: 21 pages, 5 figures, Journal of Physics: Condensed Matter, 24,
116002, (2012
The Yang-Baxter equation for PT invariant nineteen vertex models
We study the solutions of the Yang-Baxter equation associated to nineteen
vertex models invariant by the parity-time symmetry from the perspective of
algebraic geometry. We determine the form of the algebraic curves constraining
the respective Boltzmann weights and found that they possess a universal
structure. This allows us to classify the integrable manifolds in four
different families reproducing three known models besides uncovering a novel
nineteen vertex model in a unified way. The introduction of the spectral
parameter on the weights is made via the parameterization of the fundamental
algebraic curve which is a conic. The diagonalization of the transfer matrix of
the new vertex model and its thermodynamic limit properties are discussed. We
point out a connection between the form of the main curve and the nature of the
excitations of the corresponding spin-1 chains.Comment: 43 pages, 6 figures and 5 table
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