200 research outputs found
A new comprehensive study of the 3D random-field Ising model via sampling the density of states in dominant energy subspaces
The three-dimensional bimodal random-field Ising model is studied via a new
finite temperature numerical approach. The methods of Wang-Landau sampling and
broad histogram are implemented in a unified algorithm by using the N-fold
version of the Wang-Landau algorithm. The simulations are performed in dominant
energy subspaces, determined by the recently developed critical minimum energy
subspace technique. The random fields are obtained from a bimodal distribution,
that is we consider the discrete case and the model is studied on
cubic lattices with sizes . In order to extract information
for the relevant probability distributions of the specific heat and
susceptibility peaks, large samples of random field realizations are generated.
The general aspects of the model's scaling behavior are discussed and the
process of averaging finite-size anomalies in random systems is re-examined
under the prism of the lack of self-averaging of the specific heat and
susceptibility of the model.Comment: 10 pages, 4 figures, presented at the third NEXT Sigma Phi
International Conference, Kolymbari, Greece (2005
Monte Carlo studies of the square Ising model with next-nearest-neighbor interactions
We apply a new entropic scheme to study the critical behavior of the
square-lattice Ising model with nearest- and next-nearest-neighbor
antiferromagnetic interactions. Estimates of the present scheme are compared
with those of the Metropolis algorithm. We consider interactions in the range
where superantiferromagnetic (SAF) order appears at low temperatures. A recent
prediction of a first-order transition along a certain range (0.5-1.2) of the
interaction ratio is examined by generating accurate data
for large lattices at a particular value of the ratio . Our study does
not support a first-order transition and a convincing finite-size scaling
analysis of the model is presented, yielding accurate estimates for all
critical exponents for R=1 . The magnetic exponents are found to obey ``weak
universality'' in accordance with a previous conjecture.Comment: 9 pages, 7 figures, Proceedings of the third NEXT Sigma Phi
International Conference, kolymbari, Greece (2005
Critical behavior of hard-core lattice gases: Wang-Landau sampling with adaptive windows
Critical properties of lattice gases with nearest-neighbor exclusion are
investigated via the adaptive-window Wang-Landau algorithm on the square and
simple cubic lattices, for which the model is known to exhibit an Ising-like
phase transition. We study the particle density, order parameter,
compressibility, Binder cumulant and susceptibility. Our results show that it
is possible to estimate critical exponents using Wang-Landau sampling with
adaptive windows. Finite-size-scaling analysis leads to results in fair
agreement with exact values (in two dimensions) and numerical estimates (in
three dimensions).Comment: 20 pages, 11 figure
Universality aspects of the d=3 random-bond Blume-Capel model
The effects of bond randomness on the universality aspects of the simple
cubic lattice ferromagnetic Blume-Capel model are discussed. The system is
studied numerically in both its first- and second-order phase transition
regimes by a comprehensive finite-size scaling analysis. We find that our data
for the second-order phase transition, emerging under random bonds from the
second-order regime of the pure model, are compatible with the universality
class of the 3d random Ising model. Furthermore, we find evidence that, the
second-order transition emerging under bond randomness from the first-order
regime of the pure model, belongs to a new and distinctive universality class.
The first finding reinforces the scenario of a single universality class for
the 3d Ising model with the three well-known types of quenched uncorrelated
disorder (bond randomness, site- and bond-dilution). The second, amounts to a
strong violation of universality principle of critical phenomena. For this case
of the ex-first-order 3d Blume-Capel model, we find sharp differences from the
critical behaviors, emerging under randomness, in the cases of the
ex-first-order transitions of the corresponding weak and strong first-order
transitions in the 3d three-state and four-state Potts models.Comment: 12 pages, 12 figure
Criticality in the randomness-induced second-order phase transition of the triangular Ising antiferromagnet with nearest- and next-nearest-neighbor interactions
Using a Wang-Landau entropic sampling scheme, we investigate the effects of
quenched bond randomness on a particular case of a triangular Ising model with
nearest- () and next-nearest-neighbor () antiferromagnetic
interactions. We consider the case , for which the pure
model is known to have a columnar ground state where rows of nearest-neighbor
spins up and down alternate and undergoes a weak first-order phase transition
from the ordered to the paramagnetic state. With the introduction of quenched
bond randomness we observe the effects signaling the expected conversion of the
first-order phase transition to a second-order phase transition and using the
Lee-Kosterlitz method, we quantitatively verify this conversion. The emerging,
under random bonds, continuous transition shows a strongly saturating specific
heat behavior, corresponding to a negative exponent , and belongs to a
new distinctive universality class with , ,
and . Thus, our results for the critical exponents support
an extensive but weak universality and the emerged continuous transition has
the same magnetic critical exponent (but a different thermal critical exponent)
as a wide variety of two-dimensional (2d) systems without and with quenched
disorder.Comment: 17 pages, 6 figures, accepted for publication in Physica
Uncovering the secrets of the 2d random-bond Blume-Capel model
The effects of bond randomness on the ground-state structure, phase diagram
and critical behavior of the square lattice ferromagnetic Blume-Capel (BC)
model are discussed. The calculation of ground states at strong disorder and
large values of the crystal field is carried out by mapping the system onto a
network and we search for a minimum cut by a maximum flow method. In finite
temperatures the system is studied by an efficient two-stage Wang-Landau (WL)
method for several values of the crystal field, including both the first- and
second-order phase transition regimes of the pure model. We attempt to explain
the enhancement of ferromagnetic order and we discuss the critical behavior of
the random-bond model. Our results provide evidence for a strong violation of
universality along the second-order phase transition line of the random-bond
version.Comment: 6 LATEX pages, 3 EPS figures, Presented by AM at the symposium
"Trajectories and Friends" in honor of Nihat Berker, MIT, October 200
Wang-Landau study of the critical behaviour of the bimodal 3D-Random Field Ising Model
We apply the Wang-Landau method to the study of the critical behaviour of the
three dimensional Random Field Ising Model with a bimodal probability
distribution. Our results show that for high values of the random field
intensity the transition is first order, characterized by a double-peaked
energy probability distribution at the transition temperature. On the other
hand, the transition looks continuous for low values of the field intensity. In
spite of the large sample to sample fluctuations observed, the double peak in
the probability distribution is always present for high field
Phase Diagram of the 3D Bimodal Random-Field Ising Model
The one-parametric Wang-Landau (WL) method is implemented together with an
extrapolation scheme to yield approximations of the two-dimensional
(exchange-energy, field-energy) density of states (DOS) of the 3D bimodal
random-field Ising model (RFIM). The present approach generalizes our earlier
WL implementations, by handling the final stage of the WL process as an
entropic sampling scheme, appropriate for the recording of the required
two-parametric histograms. We test the accuracy of the proposed extrapolation
scheme and then apply it to study the size-shift behavior of the phase diagram
of the 3D bimodal RFIM. We present a finite-size converging approach and a
well-behaved sequence of estimates for the critical disorder strength. Their
asymptotic shift-behavior yields the critical disorder strength and the
associated correlation length's exponent, in agreement with previous estimates
from ground-state studies of the model.Comment: 18 pages, 7 figure
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