We employ the functional renormalization group framework at the second order in the derivative expansion to study the O(N)O(N) models continuously varying the number of field components NN and the spatial dimensionality dd. We in particular address the Cardy-Hamber prediction concerning nonanalytical behavior of the critical exponents \nuν and \etaη across a line in the (d,N)(d,N) plane, which passes through the point (2,2)(2,2). By direct numerical evaluation of \eta(d,N)η(d,N) and \nu^{-1}(d,N)ν−1(d,N) as well as analysis of the functional fixed-point profiles, we find clear indications of this line in the form of a crossover between two regimes in the (d,N)(d,N) plane, however no evidence of discontinuous or singular first and second derivatives of these functions for d>2d>2. The computed derivatives of \eta(d,N)η(d,N) and \nu^{-1}(d,N)ν−1(d,N) become increasingly large for d\to 2d→2 and N\to 2N→2 and it is only in this limit that \eta(d,N)η(d,N) and \nu^{-1}(d,N)ν−1(d,N) as obtained by us are evidently nonanalytical. By scanning the dependence of the subleading eigenvalue of the RG transformation on NN for d>2d>2 we find no indication of its vanishing as anticipated by the Cardy-Hamber scenario. For dimensionality dd approaching 3 there are no signatures of the Cardy-Hamber line even as a crossover and its existence in the form of a nonanalyticity of the anticipated form is excluded.
The classical, in its nature, concept of atomic or ionic radii, although profitable in many fields, is represented by an ambiguous choice of formulations. In this work, we propose a definition of atomic and ionic radii rooted in chemical principles and conceptual density functional theories. The estimation based on electron density fundamental response functions has been successfully tested. The generalized approach has been shown to be applicable to atoms in any oxidation state. The radii display good correlation with classical estimates, such as Shannon. The atomic and ionic radii obtained according to this scheme are directly comparable between different elements, without any adjustment procedures requiring fitting constants. The definition also has a clear physical interpretation, which supports understanding of size-related phenomena and trends.
We study the O(2) model with Z 4 -symmetric perturbations within the framework of nonperturbative renormalization group (RG) for spatial dimensionality d = 2 and d = 3. In a unified framework we resolve the relatively complex crossover behavior emergent due to the presence of multiple RG fixed points. In d = 3 the system is controlled by the XY, Ising, and low-T fixed points in presence of a dangerously irrelevant anisotropy coupling λ. In d = 2 the anisotropy coupling is marginal and the physical picture is governed by the interplay between two distinct lines of RG fixed points, giving rise to nonuniversal critical behavior; and an isolated Ising fixed point. In addition to inducing crossover behavior in universal properties, the presence of the Ising fixed point yields a generic, abrupt change of critical temperature at a specific value of the anisotropy field.
Introduction: The purpose of this study was to introduce a measure of patient's burden based on Elixhauser's comorbidity index. The mentioned measure needed to be based solely on administrative data and be applicable to all specialisations of hospital treatment. Moreover, the intention was to validate the estimation power of the models based on the groups of hospitalisations which were similar with respect to the primary diagnosis. Material and methods: In the study, we considered all hospitalisations in Poland from 2014 and 2015. Overall, 22 045 267 hospitalisation records of 11 566 525 patients were retrieved. An important element of this research was to validate the estimation power of the models based on the groups of patients who were similar with respect to the main reason for hospitalisation. Therefore, the population was split into 21 Homogeneous Groups based on the changed primary diagnosis. As explanatory variables we used demographic variables and 31 comorbidities defined by Elixhauser. The outcome variable was patient's mortality-in-hospital or up to 365 days after discharge. Results: Out of the 21 created models, 9 had a very good estimation power (C-statistic over 0.85), the other 9 had satysfying results (C-statistic between 0.75 and 0.85) and only 3 performed poorly (C-statistic below 0.75). The odds ratio of variables varied widely between the groups. Conclusions: Our results support the hypothesis that comorbidity properly describes mortality in homogeneous groups of patients. Our models could be condensed into one, uniform, single-number comorbidity scale that summarizes all of the patient's burden. It was found that the odds ratio of some variables differed between homogeneous groups.
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