1,887 research outputs found
Site-diluted three dimensional Ising Model with long-range correlated disorder
We study two different versions of the site-diluted Ising model in three
dimensions with long-range spatially correlated disorder by Monte Carlo means.
We use finite-size scaling techniques to compute the critical exponents of
these systems, taking into account the strong scaling-corrections. We find a
value that is compatible with the analytical predictions.Comment: 19 pages, 1 postscript figur
Superintegrability on sl(2)-coalgebra spaces
We review a recently introduced set of N-dimensional quasi-maximally
superintegrable Hamiltonian systems describing geodesic motions, that can be
used to generate "dynamically" a large family of curved spaces. From an
algebraic viewpoint, such spaces are obtained through kinetic energy
Hamiltonians defined on either the sl(2) Poisson coalgebra or a quantum
deformation of it. Certain potentials on these spaces and endowed with the same
underlying coalgebra symmetry have been also introduced in such a way that the
superintegrability properties of the full system are preserved. Several new N=2
examples of this construction are explicitly given, and specific Hamiltonians
leading to spaces of non-constant curvature are emphasized.Comment: 12 pages. Based on the contribution presented at the "XII
International Conference on Symmetry Methods in Physics", Yerevan (Armenia),
July 2006. To appear in Physics of Atomic Nucle
Universal integrals for superintegrable systems on N-dimensional spaces of constant curvature
An infinite family of classical superintegrable Hamiltonians defined on the
N-dimensional spherical, Euclidean and hyperbolic spaces are shown to have a
common set of (2N-3) functionally independent constants of the motion. Among
them, two different subsets of N integrals in involution (including the
Hamiltonian) can always be explicitly identified. As particular cases, we
recover in a straightforward way most of the superintegrability properties of
the Smorodinsky-Winternitz and generalized Kepler-Coulomb systems on spaces of
constant curvature and we introduce as well new classes of (quasi-maximally)
superintegrable potentials on these spaces. Results here presented are a
consequence of the sl(2) Poisson coalgebra symmetry of all the Hamiltonians,
together with an appropriate use of the phase spaces associated to Poincare and
Beltrami coordinates.Comment: 12 page
Binary trees, coproducts, and integrable systems
We provide a unified framework for the treatment of special integrable
systems which we propose to call "generalized mean field systems". Thereby
previous results on integrable classical and quantum systems are generalized.
Following Ballesteros and Ragnisco, the framework consists of a unital algebra
with brackets, a Casimir element, and a coproduct which can be lifted to higher
tensor products. The coupling scheme of the iterated tensor product is encoded
in a binary tree. The theory is exemplified by the case of a spin octahedron.Comment: 15 pages, 6 figures, v2: minor correction in theorem 1, two new
appendices adde
Correlation length of the two-dimensional Ising spin glass with bimodal interactions
We study the correlation length of the two-dimensional Edwards-Anderson Ising
spin glass with bimodal interactions using a combination of parallel tempering
Monte Carlo and a rejection-free cluster algorithm in order to speed up
equilibration. Our results show that the correlation length grows ~ exp(2J/T)
suggesting through hyperscaling that the degenerate ground state is separated
from the first excited state by an energy gap ~4J, as would naively be
expected.Comment: 5 pages, 4 figures, 2 table
Antiferromagnetic O(N) models in four dimensions
We study the antiferromagnetic O(N) model in the F_4 lattice. Monte Carlo
simulations are applied for investigating the behavior of the transition for
N=2,3. The numerical results show a first order nature but with a large
correlation length. The limit is also considered with analytical
methods.Comment: 14 pages, 3 postscript figure
Classical Lie algebras and Drinfeld doubles
The Drinfeld double structure underlying the Cartan series An, Bn, Cn, Dn of
simple Lie algebras is discussed.
This structure is determined by two disjoint solvable subalgebras matched by
a pairing. For the two nilpotent positive and negative root subalgebras the
pairing is natural and in the Cartan subalgebra is defined with the help of a
central extension of the algebra.
A new completely determined basis is found from the compatibility conditions
in the double and a different perspective for quantization is presented. Other
related Drinfeld doubles on C are also considered.Comment: 11 pages. submitted for publication to J. Physics
Non-coboundary Poisson-Lie structures on the book group
All possible Poisson-Lie (PL) structures on the 3D real Lie group generated
by a dilation and two commuting translations are obtained. Its classification
is fully performed by relating these PL groups with the corresponding Lie
bialgebra structures on the corresponding "book" Lie algebra. By construction,
all these Poisson structures are quadratic Poisson-Hopf algebras for which the
group multiplication is a Poisson map. In contrast to the case of simple Lie
groups, it turns out that most of the PL structures on the book group are
non-coboundary ones. Moreover, from the viewpoint of Poisson dynamics, the most
interesting PL book structures are just some of these non-coboundaries, which
are explicitly analysed. In particular, we show that the two different
q-deformed Poisson versions of the sl(2,R) algebra appear as two distinguished
cases in this classification, as well as the quadratic Poisson structure that
underlies the integrability of a large class of 3D Lotka-Volterra equations.
Finally, the quantization problem for these PL groups is sketched.Comment: 15 pages, revised version, some references adde
Universal --matrices for non-standard (1+1) quantum groups
A universal quasitriangular --matrix for the non-standard quantum (1+1)
Poincar\'e algebra is deduced by imposing analyticity in the
deformation parameter . A family of ``quantum graded contractions"
of the algebra is obtained; this set of
quantum algebras contains as Hopf subalgebras with two primitive translations
quantum analogues of the two dimensional Euclidean, Poincar\'e and Galilei
algebras enlarged with dilations. Universal --matrices
for these quantum Weyl algebras and their associated quantum groups are
constructed.Comment: 12 pages, LaTeX
Critical Exponents of the 3D Ising Universality Class From Finite Size Scaling With Standard and Improved Actions
We propose a method to obtain an improved Hamiltonian (action) for the Ising
universality class in three dimensions. The improved Hamiltonian has suppressed
leading corrections to scaling. It is obtained by tuning models with two
coupling constants. We studied three different models: the +1,-1 Ising model
with nearest neighbour and body diagonal interaction, the spin-1 model with
states 0,+1,-1, and nearest neighbour interaction, and phi**4-theory on the
lattice (Landau-Ginzburg Hamiltonian). The remarkable finite size scaling
properties of the suitably tuned spin-1 model are compared in detail with those
of the standard Ising model. Great care is taken to estimate the systematic
errors from residual corrections to scaling. Our best estimates for the
critical exponents are nu= 0.6298(5) and eta= 0.0366(8), where the given error
estimates take into account the statistical and systematic uncertainties.Comment: 55 pages, 12 figure
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