12 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 study of the interfacial adsorption of the Blume-Capel model
We investigate the scaling of the interfacial adsorption of the
two-dimensional Blume-Capel model using Monte Carlo simulations. In particular,
we study the finite-size scaling behavior of the interfacial adsorption of the
pure model at both its first- and second-order transition regimes, as well as
at the vicinity of the tricritical point. Our analysis benefits from the
currently existing quite accurate estimates of the relevant (tri)critical-point
locations. In all studied cases, the numerical results verify to a level of
high accuracy the expected scenarios derived from analytic free-energy scaling
arguments. We also investigate the size dependence of the interfacial
adsorption under the presence of quenched bond randomness at the originally
first-order transition regime (disorder-induced continuous transition) and the
relevant self-averaging properties of the system. For this ex-first-order
regime, where strong transient effects are shown to be present, our findings
support the scenario of a non-divergent scaling, similar to that found in the
original second-order transition regime of the pure model.Comment: 6 pages, 5 figures, version published in Phys. Rev. E. arXiv admin
note: text overlap with arXiv:1610.0822
Multicanonical simulations of the 2D spin-1 Baxter-Wu model in a crystal field
We investigate aspects of universality in the two-dimensional (2D) spin-
Baxter-Wu model in a crystal field using a parallel version of the
multicanonical algorithm employed at constant temperature . A detailed
finite-size scaling analysis in the continuous regime of the phase
diagram of the model indicates that the transition belongs to the universality
class of the -state Potts model. The presence of first-order-like
finite-size effects that become more pronounced as one approaches the
pentacritical point of the model is highlighted and discussed.Comment: 6 pages, 6 figures, XXXII IUPAP Conference on Computational Physic
Critical behavior of the pure and random-bond two-dimensional triangular Ising ferromagnet
We investigate the effects of quenched bond randomness on the critical
properties of the two-dimensional ferromagnetic Ising model embedded in a
triangular lattice. The system is studied in both the pure and disordered
versions by the same efficient two-stage Wang-Landau method. In the first part
of our study we present the finite-size scaling behavior of the pure model, for
which we calculate the critical amplitude of the specific heat's logarithmic
expansion. For the disordered system, the numerical data and the relevant
detailed finite-size scaling analysis along the lines of the two well-known
scenarios - logarithmic corrections versus weak universality - strongly support
the field-theoretically predicted scenario of logarithmic corrections. A
particular interest is paid to the sample-to-sample fluctuations of the random
model and their scaling behavior that are used as a successful alternative
approach to criticality.Comment: 10 pages, 8 figures, slightly revised version as accepted for
publication in Phys. Rev.
Interfacial adsorption in two-dimensional pure and random-bond Potts models
We study using Monte Carlo simulations the finite-size scaling behavior of
the interfacial adsorption of the two-dimensional square-lattice -states
Potts model. We consider the pure and random-bond versions of the Potts model
for and , thus probing the interfacial properties at the
originally continuous, weak, and strong first-order phase transitions. For the
pure systems our results support the early scaling predictions for the size
dependence of the interfacial adsorption at both first- and second-order phase
transitions. For the disordered systems, the interfacial adsorption at the
(disordered induced) continuous transitions is discussed, applying standard
scaling arguments and invoking findings for bulk critical properties. The
self-averaging properties of the interfacial adsorption are also analyzed by
studying the infinite limit-size extrapolation of properly defined
signal-to-noise ratios.Comment: 7 pages, 5 figures, final version to be published in Phys. Rev. E.
arXiv admin note: text overlap with arXiv:1504.0742
Lack of self-averaging of the specific heat in the three-dimensional random-field Ising model
We apply the recently developed critical minimum energy subspace scheme for
the investigation of the random-field Ising model. We point out that this
method is well suited for the study of this model. The density of states is
obtained via the Wang-Landau and broad histogram methods in a unified
implementation by employing the N-fold version of the Wang-Landau scheme. The
random-fields are obtained from a bimodal distribution (), and the
scaling of the specific heat maxima is studied on cubic lattices with sizes
ranging from to . Observing the finite-size scaling behavior of the
maxima of the specific heats we examine the question of saturation of the
specific heat. The lack of self-averaging of this quantity is fully illustrated
and it is shown that this property may be related to the question mentioned
above.Comment: 8 pages, 7 figures, extended version with two new figures, version as
accepted for publication to Physical Review
Critical Binder cumulant and universality: Fortuin-Kasteleyn clusters and order-parameter fluctuations
We investigate the dependence of the critical Binder cumulant of the
magnetization and the largest Fortuin-Kasteleyn cluster on the boundary
conditions and aspect ratio of the underlying square Ising lattices. By means
of the Swendsen-Wang algorithm, we generate numerical data for large system
sizes and we perform a detailed finite-size scaling analysis for several values
of the aspect ratio , for both periodic and free boundary conditions. We
estimate the universal probability density functions of the largest
Fortuin-Kasteleyn cluster and we compare it to those of the magnetization at
criticality. It is shown that these probability density functions follow
similar scaling laws, and it is found that the values of the critical Binder
cumulant of the largest Fortuin-Kasteleyn cluster are upper bounds to the
values of the respective order-parameter's cumulant, with a splitting behavior
for large values of the aspect ratio. We also investigate the dependence of the
amplitudes of the magnetization and the largest Fortuin-Kasteleyn cluster on
the aspect ratio and boundary conditions. We find that the associated
exponents, describing the aspect ratio dependencies, are different for the
magnetization and the largest Fortuin-Kasteleyn cluster, but in each case are
independent of boundary conditions.Comment: 8 pages, 8 figures, 2 tables, version as published in Phys Rev
Universal features and tail analysis of the order-parameter distribution of the two-dimensional Ising model: An entropic sampling Monte Carlo study
We present a numerical study of the order-parameter probability density
function (PDF) of the square Ising model for lattices with linear sizes
. A recent efficient entropic sampling scheme, combining the
Wang-Landau and broad histogram methods and based on the high-levels of the
Wang-Landau process in dominant energy subspaces is employed. We find that for
large lattices there exists a stable window of the scaled order-parameter in
which the full ansatz including the pre-exponential factor for the tail regime
of the universal PDF is well obeyed. This window is used to estimate the
equation of state exponent and to observe the behavior of the universal
constants implicit in the functional form of the universal PDF. The probability
densities are used to estimate the universal Privman-Fisher coefficient and to
investigate whether one could obtain reliable estimates of the universal
constants controlling the asymptotic behavior of the tail regime.Comment: 24 pages, 5 figure
Scaling and universality in the phase diagram of the 2D Blume-Capel model
We review the pertinent features of the phase diagram of the zero-field
Blume-Capel model, focusing on the aspects of transition order, finite-size
scaling and universality. In particular, we employ a range of Monte Carlo
simulation methods to study the 2D spin-1 Blume-Capel model on the square
lattice to investigate the behavior in the vicinity of the first-order and
second-order regimes of the ferromagnet-paramagnet phase boundary,
respectively. To achieve high-precision results, we utilize a combination of
(i) a parallel version of the multicanonical algorithm and (ii) a hybrid
updating scheme combining Metropolis and generalized Wolff cluster moves. These
techniques are combined to study for the first time the correlation length of
the model, using its scaling in the regime of second-order transitions to
illustrate universality through the observed identity of the limiting value of
with the exactly known result for the Ising universality class.Comment: 16 pages, 7 figures, 1 table, submitted to Eur. Phys. J. Special
Topic
Critical aspects of three-dimensional anisotropic spin-glass models
We study the three-dimensional Ising model with a longitudinal
anisotropic bond randomness on the simple cubic lattice. The random exchange
interaction is applied only in the direction, whereas in the other two
directions, - planes, we consider ferromagnetic exchange. By implementing
an effective parallel tempering scheme, we outline the phase diagram of the
model and compare it to the corresponding isotropic one, as well as to a
previously studied anisotropic (transverse) case. We present a detailed
finite-size scaling analysis of the ferromagnetic - paramagnetic and spin glass
- paramagnetic transition lines, and we also discuss the ferromagnetic - spin
glass transition regime. We conclude that the present model shares the same
universality classes with the isotropic model, but at the symmetric point has a
considerably higher transition temperature from the spin-glass state to the
paramagnetic phase. Our data for the ferromagnetic - spin glass transition line
are supporting a forward behavior in contrast to the reentrant behavior of the
isotropic model.Comment: 10 pages, 9 eps figures, 1 table, corrected symbolis