269 research outputs found
The U(1)A anomaly in noncommutative SU(N) theories
We work out the one-loop anomaly for noncommutative SU(N) gauge
theories up to second order in the noncommutative parameter .
We set and conclude that there is no breaking of the classical
symmetry of the theory coming from the contributions that are either
linear or quadratic in . Of course, the ordinary anomalous
contributions will be still with us. We also show that the one-loop
conservation of the nonsinglet currents holds at least up to second order in
. We adapt our results to noncommutative gauge theories with
SO(N) and U(1) gauge groups.Comment: 50 pages, 5 figures in eps files. Some comments and references adde
Long-range effects in granular avalanching
We introduce a model for granular flow in a one-dimensional rice pile that
incorporates rolling effects through a long-range rolling probability for the
individual rice grains proportional to , being the distance
traveled by a grain in a single topling event. The exponent controls the
average rolling distance. We have shown that the crossover from power law to
stretched exponential behaviors observed experimentally in the granular
dynamics of rice piles can be well described as a long-range effect resulting
from a change in the transport properties of individual grains. We showed that
stretched exponential avalanche distributions can be associated with a
long-range regime for where the average rolling distance grows as a
power law with the system size, while power law distributions are associated
with a short range regime for , where the average rolling distance is
independent of the system size.Comment: 5 pages, 3 figure
Ising nematic phase in ultra-thin magnetic films: a Monte Carlo study
We study the critical properties of a two--dimensional Ising model with
competing ferromagnetic exchange and dipolar interactions, which models an
ultra-thin magnetic film with high out--of--plane anisotropy in the monolayer
limit. We present numerical evidence showing that two different scenarios
appear in the model for different values of the exchange to dipolar intensities
ratio, namely, a single first order stripe - tetragonal phase transition or two
phase transitions at different temperatures with an intermediate Ising nematic
phase between the stripe and the tetragonal ones. Our results are very similar
to those predicted by Abanov et al [Phys. Rev. B 51, 1023 (1995)], but suggest
a much more complex critical behavior than the predicted by those authors for
both the stripe-nematic and the nematic-tetragonal phase transitions.
We also show that the presence of diverging free energy barriers at the
stripe-nematic transition makes possible to obtain by slow cooling a metastable
supercooled nematic state down to temperatures well below the transition one.Comment: 13 pages, 19 figure
Interplay between coarsening and nucleation in an Ising model with dipolar interactions
We study the dynamical behavior of a square lattice Ising model with exchange
and dipolar interactions by means of Monte Carlo simulations. After a sudden
quench to low temperatures we find that the system may undergo a coarsening
process where stripe phases with different orientations compete or
alternatively it can relax initially to a metastable nematic phase and then
decay to the equilibrium stripe phase through nucleation. We measure the
distribution of equilibration times for both processes and compute their
relative probability of occurrence as a function of temperature and system
size. This peculiar relaxation mechanism is due to the strong metastability of
the nematic phase, which goes deep in the low temperature stripe phase. We also
measure quasi-equilibrium autocorrelations in a wide range of temperatures.
They show a distinct decay to a plateau that we identify as due to a finite
fraction of frozen spins in the nematic phase. We find indications that the
plateau is a finite size effect. Relaxation times as a function of temperature
in the metastable region show super-Arrhenius behavior, suggesting a possible
glassy behavior of the system at low temperatures
Non-equilibrium structures and slow dynamics in a two dimensional spin system with competitive long range and short range interactions
We introduce a lattice spin model that mimics a system of interacting
particle through a short range repulsive potential and a long range attractive
power law decaying potential. We performed a detailed analysis of the general
equilibrium phase diagram of the model at finite temperature, showing that the
only possible equilibrium pases are the ferromagnetic and the antiferromagnetic
ones. We then studied the non equilibrium behavior of the model after a quench
to subcritical temperatures, in the antiferromagnetic region of the phase
diagram region, where the pair interaction potential behaves in the same
qualitative way as in a Lennard-Jones gas. We found that, even in the absence
of quenched disorder or geometric frustration, the competition between
interactions gives rise to non--equilibrium disordered structures at low enough
temperatures that strongly slow down the relaxation of the system.Comment: 14 pages, 20 figure
Testing boundary conditions efficiency in simulations of long-range interacting magnetic models
Periodic boundary conditions have not a unique implementation in magnetic
systems where all spins interact with each other through a power law decaying
interaction of the form , being the distance between spins. In
this work we present a comparative study of the finite size effects oberved in
numerical simulations by using first image convention and full infinite of
periodic boundary conditions in one and two-dimensional spin systems with those
type of interactions, including the ferromagnetic, antiferromagnetic and
competitive interactions cases. Our results show no significative differences
between the finite size effects produced by both types of boundary conditions
when the low temperature phase has zero global magnetization, while it depends
on the ratio for systems with a low temperature ferromagnetic phase.
In the last case the first image convention gives much more stronger finite
size effects than the other when the system enters into the classical regime
.Comment: 9 pages, 5 figure
Damage spreading in random field systems
We investigate how a quenched random field influences the damage spreading
transition in kinetic Ising models. To this end we generalize a recent master
equation approach and derive an effective field theory for damage spreading in
random field systems. This theory is applied to the Glauber Ising model with a
bimodal random field distribution. We find that the random field influences the
spreading transition by two different mechanisms with opposite effects. First,
the random field favors the same particular direction of the spin variable at
each site in both systems which reduces the damage. Second, the random field
suppresses the magnetization which, in turn, tends to increase the damage. The
competition between these two effects leads to a rich behavior.Comment: 4 pages RevTeX, 3 eps figure
Dynamical properties of the hypercell spin glass model
The spreading of damage technique is used to study the sensibility to initial
conditions in a heath bath Monte Carlo simulation of the spin glass hypercubic
cell model. Since the hypercubic cell in dimension 2D and the hypercubic
lattice in dimension D resemble each other closely at finite dimensions and
both converge to mean field when dimension goes to infinity, it allows us to
study the effect of dimensionality on the dynamical behavior of spin glasses.Comment: 13 pages, RevTex, 8 ps figure
First and second order clustering transitions for a system with infinite-range attractive interaction
We consider a Hamiltonian system made of classical particles moving in
two dimensions, coupled via an {\it infinite-range interaction} gauged by a
parameter . This system shows a low energy phase with most of the particles
trapped in a unique cluster. At higher energy it exhibits a transition towards
a homogenous phase. For sufficiently strong coupling an intermediate phase
characterized by two clusters appears. Depending on the value of the
observed transitions can be either second or first order in the canonical
ensemble. In the latter case microcanonical results differ dramatically from
canonical ones. However, a canonical analysis, extended to metastable and
unstable states, is able to describe the microcanonical equilibrium phase. In
particular, a microcanonical negative specific heat regime is observed in the
proximity of the transition whenever it is canonically discontinuous. In this
regime, {\it microcanonically stable} states are shown to correspond to {\it
saddles} of the Helmholtz free energy, located inside the spinodal region.Comment: 4 pages, Latex - 3 EPS Figs - Submitted to Phys. Rev.
Aging in a Two-Dimensional Ising Model with Dipolar Interactions
Aging in a two-dimensional Ising spin model with both ferromagnetic exchange
and antiferromagnetic dipolar interactions is established and investigated via
Monte Carlo simulations. The behaviour of the autocorrelation function
is analyzed for different values of the temperature, the waiting
time and the quotient , and being the
strength of exchange and dipolar interactions respectively. Different
behaviours are encountered for at low temperatures as is
varied. Our results show that, depending on the value of , the dynamics
of this non-disordered model is consistent either with a slow domain dynamics
characteristic of ferromagnets or with an activated scenario, like that
proposed for spin glasses.Comment: 4 pages, RevTex, 5 postscript figures; acknowledgment added and some
grammatical corrections in caption
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