12,713 research outputs found
Scaling Properties of Parallelized Multicanonical Simulations
We implemented a parallel version of the multicanonical algorithm and applied
it to a variety of systems with phase transitions of first and second order.
The parallelization relies on independent equilibrium simulations that only
communicate when the multicanonical weight function is updated. That way, the
Markov chains efficiently sample the temporary distributions allowing for good
estimations of consecutive weight functions.
The systems investigated range from the well known Ising and Potts spin
systems to bead-spring polymers. We estimate the speedup with increasing number
of parallel processes. Overall, the parallelization is shown to scale quite
well. In the case of multicanonical simulations of the -state Potts model
() and multimagnetic simulations of the Ising model, the optimal
performance is limited due to emerging barriers.Comment: Contribution to the Proceedings of "Recent Developments in Computer
Simulational Studies in Condensed Matter Physics 2013
Geometrical aspects of integrable systems
We review some basic theorems on integrability of Hamiltonian systems, namely
the Liouville-Arnold theorem on complete integrability, the Nekhoroshev theorem
on partial integrability and the Mishchenko-Fomenko theorem on noncommutative
integrability, and for each of them we give a version suitable for the
noncompact case. We give a possible global version of the previous local
results, under certain topological hypotheses on the base space. It turns out
that locally affine structures arise naturally in this setting.Comment: It will appear on International Journal of Geometric Methods in
Modern Physics vol.5 n.3 (May 2008) issu
Remnant group of local Lorentz transformations in f(T) theories
It is shown that the extended teleparallel gravitational theories, known as
f(T) theories, inherit some on shell local Lorentz invariance associated with
the tetrad field defining the spacetime structure. We discuss some enlightening
examples, such as Minkowski spacetime and cosmological
(Friedmann-Robertson-Walker and Bianchi type I) manifolds. In the first case,
we show that the absence of gravity reveals itself as an incapability in the
selection of a preferred parallelization at a local level, due to the fact that
the infinitesimal local Lorentz subgroup acts as a symmetry group of the frame
characterizing Minkowski spacetime. Finite transformations are also discussed
in these examples and, contrary to the common lore on the subject, we conclude
that the set of tetrads responsible for the parallelization of these manifolds
is quite vast and that the remnant group of local Lorentz transformations
includes one and two dimensional Abelian subgroups of the Lorentz group.Comment: 10 pages. Minor changes. To appear in PR
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