1,311 research outputs found
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
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 Point Correlation Function for the 2D Random Bond Ising Model
High accuracy Monte Carlo simulation results for 1024*1024 Ising system with
ferromagnetic impurity bonds are presented. Spin-spin correlation function at a
critical point is found to be numerically very close to that of a pure system.
This is not trivial since a critical temperature for the system with impurities
is almost two times lower than pure Ising . Finite corrections to the
correlation function due to combined action of impurities and finite lattice
size are described.Comment: 7 pages, 2 figures after LaTeX fil
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.
Scaling Analysis of the Site-Diluted Ising Model in Two Dimensions
A combination of recent numerical and theoretical advances are applied to
analyze the scaling behaviour of the site-diluted Ising model in two
dimensions, paying special attention to the implications for multiplicative
logarithmic corrections. The analysis focuses primarily on the odd sector of
the model (i.e., that associated with magnetic exponents), and in particular on
its Lee-Yang zeros, which are determined to high accuracy. Scaling relations
are used to connect to the even (thermal) sector, and a first analysis of the
density of zeros yields information on the specific heat and its corrections.
The analysis is fully supportive of the strong scaling hypothesis and of the
scaling relations for logarithmic corrections.Comment: 15 pages, 3 figures. Published versio
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
Engineering of Low-Loss Metal for Nanoplasmonic and Metamaterials Applications
We have shown that alloying a noble metal (gold) with another metal
(cadmium), which can contribute two electrons per atom to a free electron gas,
can significantly improve the metals optical properties in certain wavelength
ranges and make them worse in the other parts of the spectrum. In particular,
in the gold-cadmium alloy we have demonstrated a significant expansion of the
spectral range of metallic reflectance to shorter wavelengths. The experimental
results and the predictions of the first principles theory demonstrate an
opportunity for the improvement and optimization of low-loss metals for
nanoplasmonic and metamaterials applications.Comment: 14 Pages, 4 figure
Effects of turbulent mixing on critical behaviour in the presence of compressibility: Renormalization group analysis of two models
Critical behaviour of two systems, subjected to the turbulent mixing, is
studied by means of the field theoretic renormalization group. The first
system, described by the equilibrium model A, corresponds to relaxational
dynamics of a non-conserved order parameter. The second one is the strongly
non-equilibrium reaction-diffusion system, known as Gribov process and
equivalent to the Reggeon field theory. The turbulent mixing is modelled by the
Kazantsev-Kraichnan "rapid-change" ensemble: time-decorrelated Gaussian
velocity field with the power-like spectrum k^{-d-\xi}. Effects of
compressibility of the fluid are studied. It is shown that, depending on the
relation between the exponent \xi and the spatial dimension d, the both systems
exhibit four different types of critical behaviour, associated with four
possible fixed points of the renormalization group equations. The most
interesting point corresponds to a new type of critical behaviour, in which the
nonlinearity and turbulent mixing are both relevant, and the critical exponents
depend on d, \xi and the degree of compressibility. For the both models,
compressibility enhances the role of the nonlinear terms in the dynamical
equations: the region in the d-\xi plane, where the new nontrivial regime is
stable, is getting much wider as the degree of compressibility increases. In
its turn, turbulent transfer becomes more efficient due to combined effects of
the mixing and the nonlinear terms.Comment: 25 pages, 4 figure
Scaling Relations for Logarithmic Corrections
Multiplicative logarithmic corrections to scaling are frequently encountered
in the critical behavior of certain statistical-mechanical systems. Here, a
Lee-Yang zero approach is used to systematically analyse the exponents of such
logarithms and to propose scaling relations between them. These proposed
relations are then confronted with a variety of results from the literature.Comment: 4 page
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