1,212 research outputs found
The Site-Diluted Ising Model in Four Dimension
In the literature, there are five distinct, fragmented sets of analytic
predictions for the scaling behaviour at the phase transition in the
random-site Ising model in four dimensions. Here, the scaling relations for
logarithmic corrections are used to complete the scaling pictures for each set.
A numerical approach is then used to confirm the leading scaling picture coming
from these predictions and to discriminate between them at the level of
logarithmic corrections.Comment: 15 pages, 5 ps figures. Accepted for publication in Phys. Rev.
Observation of mixed anisotropy in the critical susceptibility of an ultrathin magnetic film
Measurements of the magnetic susceptibility of Fe/W(110) films with thickness
in the range of 1.6 to 2.4 ML Fe, show that in addition to the large response
along the easy axis associated with the Curie transition, there is a much
smaller, paramagnetic hard axis response that is not consistent with the 2D
anisotropic Heisenberg model used to describe homogeneous in-plane ferromagnets
with uniaxial anisotropy. The shape, amplitude, and peak temperature of the
hard axis susceptibility, as well as its dependence upon layer completion close
to 2.0 ML, indicate that inhomogeneities in the films create a system of mixed
anisotropy. A likely candidate for inhomogeneities that are magnetically
relevant in the critical region are the closed lines of step edges associated
with the incomplete layers. According to the Harris criterion, the existence of
magnetically relevant inhomogeneities may alter the critical properties of the
films from those of a 2D Ising model. Experiments in the recent literature are
discussed in this context.Comment: 9 two-column pages, 6 figures. This replacement has a new title and
abstract, and one additional figur
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
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
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.
Critical behavior of two-dimensional cubic and MN models in the five-loop renormalization-group approximation
The critical thermodynamics of the two-dimensional N-vector cubic and MN
models is studied within the field-theoretical renormalization-group (RG)
approach. The beta functions and critical exponents are calculated in the
five-loop approximation and the RG series obtained are resummed using the
Borel-Leroy transformation combined with the generalized Pad\'e approximant and
conformal mapping techniques. For the cubic model, the RG flows for various N
are investigated. For N=2 it is found that the continuous line of fixed points
running from the XY fixed point to the Ising one is well reproduced by the
resummed RG series and an account for the five-loop terms makes the lines of
zeros of both beta functions closer to each another. For the cubic model with
N\geq 3, the five-loop contributions are shown to shift the cubic fixed point,
given by the four-loop approximation, towards the Ising fixed point. This
confirms the idea that the existence of the cubic fixed point in two dimensions
under N>2 is an artifact of the perturbative analysis. For the quenched dilute
O(M) models ( models with N=0) the results are compatible with a stable
pure fixed point for M\geq1. For the MN model with M,N\geq2 all the
non-perturbative results are reproduced. In addition a new stable fixed point
is found for moderate values of M and N.Comment: 26 pages, 3 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
Multicritical Nishimori point in the phase diagram of the +- J Ising model on a square lattice
We investigate the critical behavior of the random-bond +- J Ising model on a
square lattice at the multicritical Nishimori point in the T-p phase diagram,
where T is the temperature and p is the disorder parameter (p=1 corresponds to
the pure Ising model). We perform a finite-size scaling analysis of
high-statistics Monte Carlo simulations along the Nishimori line defined by
, along which the multicritical point lies. The
multicritical Nishimori point is located at p^*=0.89081(7), T^*=0.9528(4), and
the renormalization-group dimensions of the operators that control the
multicritical behavior are y_1=0.655(15) and y_2 = 0.250(2); they correspond to
the thermal exponent \nu= 1/y_2=4.00(3) and to the crossover exponent \phi=
y_1/y_2=2.62(6).Comment: 23 page
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