1,381 research outputs found
q-State Potts model metastability study using optimized GPU-based Monte Carlo algorithms
We implemented a GPU based parallel code to perform Monte Carlo simulations
of the two dimensional q-state Potts model. The algorithm is based on a
checkerboard update scheme and assigns independent random numbers generators to
each thread. The implementation allows to simulate systems up to ~10^9 spins
with an average time per spin flip of 0.147ns on the fastest GPU card tested,
representing a speedup up to 155x, compared with an optimized serial code
running on a high-end CPU. The possibility of performing high speed simulations
at large enough system sizes allowed us to provide a positive numerical
evidence about the existence of metastability on very large systems based on
Binder's criterion, namely, on the existence or not of specific heat
singularities at spinodal temperatures different of the transition one.Comment: 30 pages, 7 figures. Accepted in Computer Physics Communications.
code available at:
http://www.famaf.unc.edu.ar/grupos/GPGPU/Potts/CUDAPotts.htm
Long term ordering kinetics of the two dimensional q-state Potts model
We studied the non-equilibrium dynamics of the q-state Potts model in the
square lattice, after a quench to sub-critical temperatures. By means of a
continuous time Monte Carlo algorithm (non-conserved order parameter dynamics)
we analyzed the long term behavior of the energy and relaxation time for a wide
range of quench temperatures and system sizes. For q>4 we found the existence
of different dynamical regimes, according to quench temperature range. At low
(but finite) temperatures and very long times the Lifshitz-Allen-Cahn domain
growth behavior is interrupted with finite probability when the system stuck in
highly symmetric non-equilibrium metastable states, which induce activation in
the domain growth, in agreement with early predictions of Lifshitz [JETP 42,
1354 (1962)]. Moreover, if the temperature is very low, the system always gets
stuck at short times in a highly disordered metastable states with finite life
time, which have been recently identified as glassy states. The finite size
scaling properties of the different relaxation times involved, as well as their
temperature dependency are analyzed in detail.Comment: 10 pages, 17 figure
Short-time dynamics of finite-size mean-field systems
We study the short-time dynamics of a mean-field model with non-conserved
order parameter (Curie-Weiss with Glauber dynamics) by solving the associated
Fokker-Planck equation. We obtain closed-form expressions for the first moments
of the order parameter, near to both the critical and spinodal points, starting
from different initial conditions. This allows us to confirm the validity of
the short-time dynamical scaling hypothesis in both cases. Although the
procedure is illustrated for a particular mean-field model, our results can be
straightforwardly extended to generic models with a single order parameter.Comment: accepted for publication in JSTA
Topological strings on noncommutative manifolds
We identify a deformation of the N=2 supersymmetric sigma model on a
Calabi-Yau manifold X which has the same effect on B-branes as a noncommutative
deformation of X. We show that for hyperkahler X such deformations allow one to
interpolate continuously between the A-model and the B-model. For generic
values of the noncommutativity and the B-field, properties of the topologically
twisted sigma-models can be described in terms of generalized complex
structures introduced by N. Hitchin. For example, we show that the path
integral for the deformed sigma-model is localized on generalized holomorphic
maps, whereas for the A-model and the B-model it is localized on holomorphic
and constant maps, respectively. The geometry of topological D-branes is also
best described using generalized complex structures. We also derive a
constraint on the Chern character of topological D-branes, which includes
A-branes and B-branes as special cases.Comment: 36 pages, AMS latex. v2: a reference to a related work has been
added. v3: An error in the discussion of the Fourier-Mukai transform for
twisted coherent sheaves has been fixed, resulting in several changes in
Section 2. The rest of the paper is unaffected. v4: an incorrect statement
concerning Lie algebroid cohomology has been fixe
Magnetization reversal in mixed ferrite-chromite perovskites with non magnetic cation on the A-site
In this work, we have performed Monte Carlo simulations in a classical model
for RFeCrO with R=Y and Lu, comparing the numerical simulations
with experiments and mean field calculations. In the analyzed compounds, the
antisymmetric exchange or Dzyaloshinskii-Moriya (DM) interaction induced a weak
ferromagnetism due to a canting of the antiferromagnetically ordered spins.
This model is able to reproduce the magnetization reversal (MR) observed
experimentally in a field cooling process for intermediate values and the
dependence with of the critical temperatures. We also analyzed the
conditions for the existence of MR in terms of the strength of DM interactions
between Fe and Cr ions with the x values variations.Comment: 8 pages, 7 figure
Homologous self-organising scale-invariant properties characterise long range species spread and cancer invasion
The invariance of some system properties over a range of temporal and/or spatial scales is an attribute of many processes in nature1, often characterised by power law functions and fractal geometry2. In particular, there is growing consensus in that fat-tailed functions like the power law adequately describe long-distance dispersal (LDD) spread of organisms 3,4. Here we show that the spatial spread of individuals governed by a power law dispersal function is represented by a clear and unique signature, characterised by two properties: A fractal geometry of the boundaries of patches generated by dispersal with a fractal dimension D displaying universal features, and a disrupted patch size distribution characterised by two different power laws. Analysing patterns obtained by simulations and real patterns from species dispersal and cell spread in cancer invasion we show that both pattern properties are a direct result of LDD and localised dispersal and recruitment, reflecting population self-organisation
The Lie-Poisson structure of the reduced n-body problem
The classical n-body problem in d-dimensional space is invariant under the
Galilean symmetry group. We reduce by this symmetry group using the method of
polynomial invariants. As a result we obtain a reduced system with a
Lie-Poisson structure which is isomorphic to sp(2n-2), independently of d. The
reduction preserves the natural form of the Hamiltonian as a sum of kinetic
energy that depends on velocities only and a potential that depends on
positions only. Hence we proceed to construct a Poisson integrator for the
reduced n-body problem using a splitting method.Comment: 26 pages, 2 figure
Phase separation of the Potts model in que square lattice
When the two dimensional q-color Potts model in the square lattice is
quenched at zero temperature with Glauber dynamics, the energy decreases in
time following an Allen-Cahn power law, and the system converges to a phase
with energy higher than the ground state energy after an arbitrary large time
when q>4. At low but finite temperature, it cesses to obey the power-law regime
and orders after a very long time, which increases with q, and before which it
performs a domain growth process which tends to be slower as q increases. We
briefly present and comment numerical results on the ordering at nonzero
temperature.Comment: 3 pages, 1 figure, proceedings of the "International Workshop on
Complex sytems", June 2006 in Santander (Spain
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