Functional renormalization group approach to non-collinear magnets

A functional renormalization group approach to $d$-dimensional, $N$-component, non-collinear magnets is performed using various truncations of the effective action relevant to study their long distance behavior. With help of these truncations we study the existence of a stable fixed point for dimensions between $d= 2.8$ and $d=4$ for various values of $N$ focusing on the critical value $N_c(d)$ that, for a given dimension $d$, separates a first order region for $NN_c(d)$. Our approach concludes to the absence of stable fixed point in the physical - $N=2,3$ and $d=3$ - cases, in agreement with $\epsilon=4-d$-expansion and in contradiction with previous perturbative approaches performed at fixed dimension and with recent approaches based on conformal bootstrap program.Comment: 16 pages, 8 figure

Model C critical dynamics of random anisotropy magnets

We study the relaxational critical dynamics of the three-dimensional random anisotropy magnets with the non-conserved n-component order parameter coupled to a conserved scalar density. In the random anisotropy magnets the structural disorder is present in a form of local quenched anisotropy axes of random orientation. When the anisotropy axes are randomly distributed along the edges of the n-dimensional hypercube, asymptotical dynamical critical properties coincide with those of the random-site Ising model. However structural disorder gives rise to considerable effects for non-asymptotic critical dynamics. We investigate this phenomenon by a field-theoretical renormalization group analysis in the two-loop order. We study critical slowing down and obtain quantitative estimates for the effective and asymptotic critical exponents of the order parameter and scalar density. The results predict complex scenarios for the effective critical exponent approaching an asymptotic regime.Comment: 8 figures, style files include

Association of maternal pancreatic function and foetal growth in rats treated with DFU, a selective cyclooxygenase-2 inhibitor

Constitutive (COX-1) and inducible (COX-2) cyclooxygenase isoforms have been detected in various mammalian tissues. Their activity is blocked by non-steroidal anti-inflammatory drugs that may induce various side reactions. The aim of the study was to evaluate the effects of DFU, a selective COX-2 inhibitor, on exocrine and endocrine pancreatic function and the immunoexpression of both COX isoforms in maternal and foetal rat pancreases. The compound was administered to pregnant Wistar rats once daily from the 8th to the 21st day of gestation. Glucose level and amylase activity were determined in the maternal sera. Maternal and foetal pancreases were examined histologically. Immunoexpression of COX-1 and COX-2 was also evaluated. Both biochemical parameters, as well as the histological structure of the pancreas were undisturbed in the dams and their foetuses. The maternal glucose level was found to be an important factor for foetal growth. Strong cytoplasmic COX-1 immunostaining was observed in acinar secretory cells, whereas in islets the immune reaction was weak. Endocrine cells also revealed strong cytoplasmic COX-2 staining in the maternal and foetal pancreases. Acinar cells exhibited nuclear reaction, which was strong in the foetal but weak in the maternal pancreases. No differences in COX immunoexpression were found between the DFU-exposed and the control groups in either mothers or foetuses. It should be stressed that DFU administered throughout mid and late pregnancy in rats did not change maternal or foetal pancreatic morphology or immunoexpression of either of the main COX isoforms in the organ

Critical dynamics and effective exponents of magnets with extended impurities

We investigate the asymptotic and effective static and dynamic critical behavior of (d=3)-dimensional magnets with quenched extended defects, correlated in $\epsilon_d$ dimensions (which can be considered as the dimensionality of the defects) and randomly distributed in the remaining $d-\epsilon_d$ dimensions. The field-theoretical renormalization group perturbative expansions being evaluated naively do not allow for the reliable numerical data. We apply the Chisholm-Borel resummation technique to restore convergence of the two-loop expansions and report the numerical values of the asymptotic critical exponents for the model A dynamics. We discuss different scenarios for static and dynamic effective critical behavior and give values for corresponding non-universal exponents.Comment: 12 pages, 6 figure

Critical behavior of disordered systems with replica symmetry breaking

A field-theoretic description of the critical behavior of weakly disordered systems with a $p$-component order parameter is given. For systems of an arbitrary dimension in the range from three to four, a renormalization group analysis of the effective replica Hamiltonian of the model with an interaction potential without replica symmetry is given in the two-loop approximation. For the case of the one-step replica symmetry breaking, fixed points of the renormalization group equations are found using the Pade-Borel summing technique. For every value $p$, the threshold dimensions of the system that separate the regions of different types of the critical behavior are found by analyzing those fixed points. Specific features of the critical behavior determined by the replica symmetry breaking are described. The results are compared with those obtained by the $\epsilon$-expansion and the scope of the method applicability is determined.Comment: 18 pages, 2 figure

Universality classes of three-dimensional mnmn-vector model

We study the conditions under which the critical behavior of the three-dimensional $mn$-vector model does not belong to the spherically symmetrical universality class. In the calculations we rely on the field-theoretical renormalization group approach in different regularization schemes adjusted by resummation and extended analysis of the series for renormalization-group functions which are known for the model in high orders of perturbation theory. The phase diagram of the three-dimensional $mn$-vector model is built marking out domains in the $mn$-plane where the model belongs to a given universality class.Comment: 9 pages, 1 figur

Critical behavior of the random-anisotropy model in the strong-anisotropy limit

We investigate the nature of the critical behavior of the random-anisotropy Heisenberg model (RAM), which describes a magnetic system with random uniaxial single-site anisotropy, such as some amorphous alloys of rare earths and transition metals. In particular, we consider the strong-anisotropy limit (SRAM), in which the Hamiltonian can be rewritten as the one of an Ising spin-glass model with correlated bond disorder. We perform Monte Carlo simulations of the SRAM on simple cubic L^3 lattices, up to L=30, measuring correlation functions of the replica-replica overlap, which is the order parameter at a glass transition. The corresponding results show critical behavior and finite-size scaling. They provide evidence of a finite-temperature continuous transition with critical exponents $\eta_o=-0.24(4)$ and $\nu_o=2.4(6)$. These results are close to the corresponding estimates that have been obtained in the usual Ising spin-glass model with uncorrelated bond disorder, suggesting that the two models belong to the same universality class. We also determine the leading correction-to-scaling exponent finding $\omega = 1.0(4)$.Comment: 24 pages, 13 figs, J. Stat. Mech. in pres

Effect of iodothyronine hormone status on doxorubicin related cardiotoxicity

The anthracycline anticancer agent doxorubicin has been recognised to induce a dose-dependent cardiotoxicity. The chronic form of such complication is characterized by an irreversible cardiac damage and congestive heart failure. Although the pathogenesis of anthracycline cardiotoxicity seems to be multifactorial, the pivotal role has been attributed to reactive oxygen species formation. Because redox equilibrium in cardiomyocytes may be regulated via iodothyronine hormones, the aim of the study was to appraise the effect of hypothyroidism on heart damages induced by doxorubicin. The rats received methimazole in drinking water (0.001 and 0.025%) after doxorubicin administration (2.0, 5.0 and 15 mg/kg). The cardiac morphology and blood biochemical markers of heart damage were assessed. Decreased levels of iodothyronine hormones had not significant impact on cardiac morphological changes and no effect on the level of B-type natriuretic peptide in rats receiving doxorubicin. Lower hormonal levels had sporadic, diverse effect on blood transaminases, lactate dehydrogenase and creatine kinase levels, but any relation to time, doxorubicin doses and hypothyroid status was found. Hypothyreosis leads to increase in fatty acid binding protein in rats receiving higher dose of doxorubicin. Hypothyreosis had no effect on heart stretching and on necrosis at morphological level, but caused biochemical symptoms of cardiomyocyte necrosis in rats receiving doxorubicin

Predicate Abstraction for Linked Data Structures

We present Alias Refinement Types (ART), a new approach to the verification of correctness properties of linked data structures. While there are many techniques for checking that a heap-manipulating program adheres to its specification, they often require that the programmer annotate the behavior of each procedure, for example, in the form of loop invariants and pre- and post-conditions. Predicate abstraction would be an attractive abstract domain for performing invariant inference, existing techniques are not able to reason about the heap with enough precision to verify functional properties of data structure manipulating programs. In this paper, we propose a technique that lifts predicate abstraction to the heap by factoring the analysis of data structures into two orthogonal components: (1) Alias Types, which reason about the physical shape of heap structures, and (2) Refinement Types, which use simple predicates from an SMT decidable theory to capture the logical or semantic properties of the structures. We prove ART sound by translating types into separation logic assertions, thus translating typing derivations in ART into separation logic proofs. We evaluate ART by implementing a tool that performs type inference for an imperative language, and empirically show, using a suite of data-structure benchmarks, that ART requires only 21% of the annotations needed by other state-of-the-art verification techniques