226 research outputs found
Five-loop \sqrt\epsilon-expansions for random Ising model and marginal spin dimensionality for cubic systems
The \sqrt\epsilon-expansions for critical exponents of the weakly-disordered
Ising model are calculated up to the five-loop order and found to possess
coefficients with irregular signs and values. The estimate n_c = 2.855 for the
marginal spin dimensionality of the cubic model is obtained by the Pade-Borel
resummation of corresponding five-loop \epsilon-expansion.Comment: 9 pages, TeX, no figure
Critical behavior of weakly-disordered anisotropic systems in two dimensions
The critical behavior of two-dimensional (2D) anisotropic systems with weak
quenched disorder described by the so-called generalized Ashkin-Teller model
(GATM) is studied. In the critical region this model is shown to be described
by a multifermion field theory similar to the Gross-Neveu model with a few
independent quartic coupling constants. Renormalization group calculations are
used to obtain the temperature dependence near the critical point of some
thermodynamic quantities and the large distance behavior of the two-spin
correlation function. The equation of state at criticality is also obtained in
this framework. We find that random models described by the GATM belong to the
same universality class as that of the two-dimensional Ising model. The
critical exponent of the correlation length for the 3- and 4-state
random-bond Potts models is also calculated in a 3-loop approximation. We show
that this exponent is given by an apparently convergent series in
(with the central charge of the Potts model) and
that the numerical values of are very close to that of the 2D Ising
model. This work therefore supports the conjecture (valid only approximately
for the 3- and 4-state Potts models) of a superuniversality for the 2D
disordered models with discrete symmetries.Comment: REVTeX, 24 pages, to appear in Phys.Rev.
Crossover and self-averaging in the two-dimensional site-diluted Ising model
Using the newly proposed probability-changing cluster (PCC) Monte Carlo
algorithm, we simulate the two-dimensional (2D) site-diluted Ising model. Since
we can tune the critical point of each random sample automatically with the PCC
algorithm, we succeed in studying the sample-dependent and the sample
average of physical quantities at each systematically. Using the
finite-size scaling (FSS) analysis for , we discuss the importance of
corrections to FSS both in the strong-dilution and weak-dilution regions. The
critical phenomena of the 2D site-diluted Ising model are shown to be
controlled by the pure fixed point. The crossover from the percolation fixed
point to the pure Ising fixed point with the system size is explicitly
demonstrated by the study of the Binder parameter. We also study the
distribution of critical temperature . Its variance shows the power-law
dependence, , and the estimate of the exponent is consistent
with the prediction of Aharony and Harris [Phys. Rev. Lett. {\bf 77}, 3700
(1996)]. Calculating the relative variance of critical magnetization at the
sample-dependent , we show that the 2D site-diluted Ising model
exhibits weak self-averaging.Comment: 6 pages including 6 eps figures, RevTeX, to appear in Phys. Rev.
Five-loop renormalization-group expansions for the three-dimensional n-vector cubic model and critical exponents for impure Ising systems
The renormalization-group (RG) functions for the three-dimensional n-vector
cubic model are calculated in the five-loop approximation. High-precision
numerical estimates for the asymptotic critical exponents of the
three-dimensional impure Ising systems are extracted from the five-loop RG
series by means of the Pade-Borel-Leroy resummation under n = 0. These
exponents are found to be: \gamma = 1.325 +/- 0.003, \eta = 0.025 +/- 0.01, \nu
= 0.671 +/- 0.005, \alpha = - 0.0125 +/- 0.008, \beta = 0.344 +/- 0.006. For
the correction-to-scaling exponent, the less accurate estimate \omega = 0.32
+/- 0.06 is obtained.Comment: 11 pages, LaTeX, no figures, published versio
Randomly dilute Ising model: A nonperturbative approach
The N-vector cubic model relevant, among others, to the physics of the
randomly dilute Ising model is analyzed in arbitrary dimension by means of an
exact renormalization-group equation. This study provides a unified picture of
its critical physics between two and four dimensions. We give the critical
exponents for the three-dimensional randomly dilute Ising model which are in
good agreement with experimental and numerical data. The relevance of the cubic
anisotropy in the O(N) model is also treated.Comment: 4 pages, published versio
Influence of uncorrelated overlayers on the magnetism in thin itinerant-electron films
The influence of uncorrelated (nonmagnetic) overlayers on the magnetic
properties of thin itinerant-electron films is investigated within the
single-band Hubbard model. The Coulomb correlation between the electrons in the
ferromagnetic layers is treated by using the spectral density approach (SDA).
It is found that the presence of nonmagnetic layers has a strong effect on the
magnetic properties of thin films. The Curie temperatures of very thin films
are modified by the uncorrelated overlayers. The quasiparticle density of
states is used to analyze the results. In addition, the coupling between the
ferromagnetic layers and the nonmagnetic layers is discussed in detail. The
coupling depends on the band occupation of the nonmagnetic layers, while it is
almost independent of the number of the nonmagnetic layers. The induced
polarization in the nonmagnetic layers shows a long-range decreasing
oscillatory behavior and it depends on the coupling between ferromagnetic and
nonmagnetic layers.Comment: 9 pages, RevTex, 6 figures, for related work see:
http://orion.physik.hu-berlin.d
The critical amplitude ratio of the susceptibility in the random-site two-dimensional Ising model
We present a new way of probing the universality class of the site-diluted
two-dimensional Ising model. We analyse Monte Carlo data for the magnetic
susceptibility, introducing a new fitting procedure in the critical region
applicable even for a single sample with quenched disorder. This gives us the
possibility to fit simultaneously the critical exponent, the critical amplitude
and the sample dependent pseudo-critical temperature. The critical amplitude
ratio of the magnetic susceptibility is seen to be independent of the
concentration of the empty sites for all investigated values of . At the same time the average effective exponent is found
to vary with the concentration , which may be argued to be due to
logarithmic corrections to the power law of the pure system. This corrections
are canceled in the susceptibility amplitude ratio as predicted by theory. The
central charge of the corresponding field theory was computed and compared well
with the theoretical predictions.Comment: 6 pages, 4 figure
Self-Averaging, Distribution of Pseudo-Critical Temperatures and Finite Size Scaling in Critical Disordered Systems
The distributions of singular thermodynamic quantities in an ensemble
of quenched random samples of linear size at the critical point are
studied by Monte Carlo in two models. Our results confirm predictions of
Aharony and Harris based on Renormalization group considerations. For an
Ashkin-Teller model with strong but irrelevant bond randomness we find that the
relative squared width, , of is weakly self averaging. , where is the specific heat exponent and is the
correlation length exponent of the pure model fixed point governing the
transition. For the site dilute Ising model on a cubic lattice, known to be
governed by a random fixed point, we find that tends to a universal
constant independent of the amount of dilution (no self averaging). However
this constant is different for canonical and grand canonical disorder. We study
the distribution of the pseudo-critical temperatures of the ensemble
defined as the temperatures of the maximum susceptibility of each sample. We
find that its variance scales as and NOT as
R_\chi\sim 70R_\chi (T_c)\chiT_c(i,l)m_i(T_c,l)T_c(i,l)(T-T_c(i,l))/T_c$. This function is found to be universal and to behave
similarly to pure systems.Comment: 31 pages, 17 figures, submitted to Phys. Rev.
Patient Reported vs Claims Based Measures of Health for Modeling Life Expectancy in Men with Prostate Cancer
PURPOSE: Life expectancy has become a core consideration in prostate cancer care. While multiple prediction tools exist to support decision making, their discriminative ability remains modest, which hampers usage and utility. We examined whether combining patient reported and claims based health measures into prediction models improves performance. MATERIALS AND METHODS: Using SEER (Surveillance, Epidemiology, and End Results)-CAHPS (Consumer Assessment of Healthcare Providers and Systems) we identified men 65 years old or older diagnosed with prostate cancer from 2004 to 2013 and extracted 4 types of data, including demographics, cancer information, claims based health measures and patient reported health measures. Next, we compared the performance of 5 nested competing risk regression models for other cause mortality. Additionally, we assessed whether adding new health measures to established prediction models improved discriminative ability. RESULTS: Among 3,240 cases 246 (7.6%) died of prostate cancer while 631 (19.5%) died of other causes. The National Cancer Institute Comorbidity Index score was associated but weakly correlated with patient reported overall health (p <0.001, r=0.21). For predicting other cause mortality the 10-year area under the receiver operating characteristic curve improved from 0.721 (demographics only) to 0.755 with cancer information and to 0.777 and 0.812 when adding claims based and patient reported health measures, respectively. The full model generated the highest value of 0.820. Models based on existing tools also improved in their performance with the incorporation of new data types as predictor variables (p <0.001). CONCLUSIONS: Prediction models for life expectancy that combine patient reported and claims based health measures outperform models that incorporate these measures separately. However, given the modest degree of improvement, the implementation of life expectancy tools should balance model performance with data availability and fidelity
The Harris-Luck criterion for random lattices
The Harris-Luck criterion judges the relevance of (potentially) spatially
correlated, quenched disorder induced by, e.g., random bonds, randomly diluted
sites or a quasi-periodicity of the lattice, for altering the critical behavior
of a coupled matter system. We investigate the applicability of this type of
criterion to the case of spin variables coupled to random lattices. Their
aptitude to alter critical behavior depends on the degree of spatial
correlations present, which is quantified by a wandering exponent. We consider
the cases of Poissonian random graphs resulting from the Voronoi-Delaunay
construction and of planar, ``fat'' Feynman diagrams and precisely
determine their wandering exponents. The resulting predictions are compared to
various exact and numerical results for the Potts model coupled to these
quenched ensembles of random graphs.Comment: 13 pages, 9 figures, 2 tables, REVTeX 4. Version as published, one
figure added for clarification, minor re-wordings and typo cleanu
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