51 research outputs found
Scaling and self-averaging in the three-dimensional random-field Ising model
We investigate, by means of extensive Monte Carlo simulations, the magnetic
critical behavior of the three-dimensional bimodal random-field Ising model at
the strong disorder regime. We present results in favor of the two-exponent
scaling scenario, , where and are the
critical exponents describing the power-law decay of the connected and
disconnected correlation functions and we illustrate, using various finite-size
measures and properly defined noise to signal ratios, the strong violation of
self-averaging of the model in the ordered phase.Comment: 8 pages, 6 figures, to be published in Eur. Phys. J.
Multicritical Points and Crossover Mediating the Strong Violation of Universality: Wang-Landau Determinations in the Random-Bond Blume-Capel model
The effects of bond randomness on the phase diagram and critical behavior of
the square lattice ferromagnetic Blume-Capel model are discussed. The system is
studied in both the pure and disordered versions by the same efficient
two-stage Wang-Landau method for many values of the crystal field, restricted
here in the second-order phase transition regime of the pure model. For the
random-bond version several disorder strengths are considered. We present phase
diagram points of both pure and random versions and for a particular disorder
strength we locate the emergence of the enhancement of ferromagnetic order
observed in an earlier study in the ex-first-order regime. The critical
properties of the pure model are contrasted and compared to those of the random
model. Accepting, for the weak random version, the assumption of the double
logarithmic scenario for the specific heat we attempt to estimate the range of
universality between the pure and random-bond models. The behavior of the
strong disorder regime is also discussed and a rather complex and yet not fully
understood behavior is observed. It is pointed out that this complexity is
related to the ground-state structure of the random-bond version.Comment: 12 pages, 11 figures, submitted for publicatio
Wang-Landau study of the 3D Ising model with bond disorder
We implement a two-stage approach of the Wang-Landau algorithm to investigate
the critical properties of the 3D Ising model with quenched bond randomness. In
particular, we consider the case where disorder couples to the nearest-neighbor
ferromagnetic interaction, in terms of a bimodal distribution of strong versus
weak bonds. Our simulations are carried out for large ensembles of disorder
realizations and lattices with linear sizes in the range . We apply
well-established finite-size scaling techniques and concepts from the scaling
theory of disordered systems to describe the nature of the phase transition of
the disordered model, departing gradually from the fixed point of the pure
system. Our analysis (based on the determination of the critical exponents)
shows that the 3D random-bond Ising model belongs to the same universality
class with the site- and bond-dilution models, providing a single universality
class for the 3D Ising model with these three types of quenched uncorrelated
disorder.Comment: 7 pages, 7 figures, to be published in Eur. Phys. J.
Strong Violation of Critical Phenomena Universality: Wang-Landau Study of the 2d Blume-Capel Model under Bond Randomness
We study the pure and random-bond versions of the square lattice
ferromagnetic Blume-Capel model, in both the first-order and second-order phase
transition regimes of the pure model. Phase transition temperatures, thermal
and magnetic critical exponents are determined for lattice sizes in the range
L=20-100 via a sophisticated two-stage numerical strategy of entropic sampling
in dominant energy subspaces, using mainly the Wang-Landau algorithm. The
second-order phase transition, emerging under random bonds from the
second-order regime of the pure model, has the same values of critical
exponents as the 2d Ising universality class, with the effect of the bond
disorder on the specific heat being well described by double-logarithmic
corrections, our findings thus supporting the marginal irrelevance of quenched
bond randomness. On the other hand, the second-order transition, emerging under
bond randomness from the first-order regime of the pure model, has a
distinctive universality class with \nu=1.30(6) and \beta/\nu=0.128(5). This
amounts to a strong violation of the universality principle of critical
phenomena, since these two second-order transitions, with different sets of
critical exponents, are between the same ferromagnetic and paramagnetic phases.
Furthermore, the latter of these two transitions supports an extensive but weak
universality, since it has the same magnetic critical exponent (but a different
thermal critical exponent) as a wide variety of two-dimensional systems. In the
conversion by bond randomness of the first-order transition of the pure system
to second order, we detect, by introducing and evaluating connectivity spin
densities, a microsegregation that also explains the increase we find in the
phase transition temperature under bond randomness.Comment: Added discussion and references. 10 pages, 6 figures. Published
versio
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.
Structural Properties of Self-Attracting Walks
Self-attracting walks (SATW) with attractive interaction u > 0 display a
swelling-collapse transition at a critical u_{\mathrm{c}} for dimensions d >=
2, analogous to the \Theta transition of polymers. We are interested in the
structure of the clusters generated by SATW below u_{\mathrm{c}} (swollen
walk), above u_{\mathrm{c}} (collapsed walk), and at u_{\mathrm{c}}, which can
be characterized by the fractal dimensions of the clusters d_{\mathrm{f}} and
their interface d_{\mathrm{I}}. Using scaling arguments and Monte Carlo
simulations, we find that for u<u_{\mathrm{c}}, the structures are in the
universality class of clusters generated by simple random walks. For
u>u_{\mathrm{c}}, the clusters are compact, i.e. d_{\mathrm{f}}=d and
d_{\mathrm{I}}=d-1. At u_{\mathrm{c}}, the SATW is in a new universality class.
The clusters are compact in both d=2 and d=3, but their interface is fractal:
d_{\mathrm{I}}=1.50\pm0.01 and 2.73\pm0.03 in d=2 and d=3, respectively. In
d=1, where the walk is collapsed for all u and no swelling-collapse transition
exists, we derive analytical expressions for the average number of visited
sites and the mean time to visit S sites.Comment: 15 pages, 8 postscript figures, submitted to Phys. Rev.
Universality of the Ising and the S=1 model on Archimedean lattices: A Monte Carlo determination
The Ising model S=1/2 and the S=1 model are studied by efficient Monte Carlo
schemes on the (3,4,6,4) and the (3,3,3,3,6) Archimedean lattices. The
algorithms used, a hybrid Metropolis-Wolff algorithm and a parallel tempering
protocol, are briefly described and compared with the simple Metropolis
algorithm. Accurate Monte Carlo data are produced at the exact critical
temperatures of the Ising model for these lattices. Their finite-size analysis
provide, with high accuracy, all critical exponents which, as expected, are the
same with the well known 2d Ising model exact values. A detailed finite-size
scaling analysis of our Monte Carlo data for the S=1 model on the same lattices
provides very clear evidence that this model obeys, also very well, the 2d
Ising model critical exponents. As a result, we find that recent Monte Carlo
simulations and attempts to define effective dimensionality for the S=1 model
on these lattices are misleading. Accurate estimates are obtained for the
critical amplitudes of the logarithmic expansions of the specific heat for both
models on the two Archimedean lattices.Comment: 9 pages, 11 figure
Wang-Landau study of the random bond square Ising model with nearest- and next-nearest-neighbor interactions
We report results of a Wang-Landau study of the random bond square Ising
model with nearest- () and next-nearest-neighbor ()
antiferromagnetic interactions. We consider the case for
which the competitive nature of interactions produces a sublattice ordering
known as superantiferromagnetism and the pure system undergoes a second-order
transition with a positive specific heat exponent . For a particular
disorder strength we study the effects of bond randomness and we find that,
while the critical exponents of the correlation length , magnetization
, and magnetic susceptibility increase when compared to the
pure model, the ratios and remain unchanged. Thus, the
disordered system obeys weak universality and hyperscaling similarly to other
two-dimensional disordered systems. However, the specific heat exhibits an
unusually strong saturating behavior which distinguishes the present case of
competing interactions from other two-dimensional random bond systems studied
previously.Comment: 9 pages, 3 figures, version as accepted for publicatio
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
- …