Critical exponents for 3D O(n)-symmetric model with n > 3

Critical exponents for the 3D O(n)-symmetric model with n > 3 are estimated on the base of six-loop renormalization-group (RG) expansions. A simple Pade-Borel technique is used for the resummation of the RG series and the Pade approximants [L/1] are shown to give rather good numerical results for all calculated quantities. For large n, the fixed point location g_c and the critical exponents are also determined directly from six-loop expansions without addressing the resummation procedure. An analysis of the numbers obtained shows that resummation becomes unnecessary when n exceeds 28 provided an accuracy of about 0.01 is adopted as satisfactory for g_c and critical exponents. Further, results of the calculations performed are used to estimate the numerical accuracy of the 1/n-expansion. The same value n = 28 is shown to play the role of the lower boundary of the domain where this approximation provides high-precision estimates for the critical exponents.Comment: 10 pages, TeX, no figure

Evaluation of the professional aptitude of a student for internship at the enterprise

The competences declared by educational standards and the labor functions declared by professional standards for compliance with each other are analyzedПроанализированы компетенции, заявленные образовательными стандартами и трудовые функции, заявленные профессиональными стандартами на предмет соответствия друг друг

Preliminary Regional Analysis of the Kaguya Lunar Radar Sounder (LRS) Data through Eastern Mare Imbrium

The Lunar Radar Sounder (LRS) experiment on board the Kaguya spacecraft is observing the subsurface structure of the Moon, using ground-penetrating radar operating in the frequency range of 5 MHz [1]. Because LRS data provides in-formation about lunar features below the surface, it allows us to improve our understanding of the processes that formed the Moon, and the post-formation changes that have occurred (such as basin formation and volcanism). We look at a swath of preliminary LRS data, that spans from 7 to 72 N, and from 2 to 10 W, passing through the eastern portion of Mare Imbrium (Figure 1). Using software, designed for the mineral exploration industry, we produce a preliminary, coarse 3D model, showing the regional structure beneath the study area. Future research will involve smaller subsets of the data in regions of interest, where finer structures, such as those identified in [2], can be studied

Современное состояние и проблемы иностранного инвестирования в Украине

В статті розглянута проблема інвестиційного забезпечення в Україні, надані основні напрямки підвищення ефективності інвестиційної діяльності, які на сучасному етапі та у перспективі мають вплинути на залучення іноземних інвестицій. Надана оцінка поточного стану інвестиційних процесів в Україні.The article deals with the problem of investment support in Ukraine, describes the main directions of improving the investment performance, now and in the near future that affect foreign investment. An assessment of the current state of the investment processes in Ukraine.В статье рассмотрена проблема инвестиционного обеспечения в Украине, описаны основные направления повышения эффективности инвестиционной деятельности, в настоящее время и в ближайшей перспективе, которые влияют на привлечение иностранных инвестиций. Дана оценка текущего состояния инвестиционных процессов в Украине

Field-theory results for three-dimensional transitions with complex symmetries

We discuss several examples of three-dimensional critical phenomena that can be described by Landau-Ginzburg-Wilson $\phi^4$ theories. We present an overview of field-theoretical results obtained from the analysis of high-order perturbative series in the frameworks of the $\epsilon$ and of the fixed-dimension d=3 expansions. In particular, we discuss the stability of the O(N)-symmetric fixed point in a generic N-component theory, the critical behaviors of randomly dilute Ising-like systems and frustrated spin systems with noncollinear order, the multicritical behavior arising from the competition of two distinct types of ordering with symmetry O($n_1$) and O($n_2$) respectively.Comment: 9 pages, Talk at the Conference TH2002, Paris, July 200

The critical behavior of frustrated spin models with noncollinear order

We study the critical behavior of frustrated spin models with noncollinear order, including stacked triangular antiferromagnets and helimagnets. For this purpose we compute the field-theoretic expansions at fixed dimension to six loops and determine their large-order behavior. For the physically relevant cases of two and three components, we show the existence of a new stable fixed point that corresponds to the conjectured chiral universality class. This contradicts previous three-loop field-theoretical results but is in agreement with experiments.Comment: 4 pages, RevTe

Chiral critical behavior in two dimensions from five-loop renormalization-group expansions

We analyse the critical behavior of two-dimensional N-vector spin systems with noncollinear order within the five-loop renormalization-group approximation. The structure of the RG flow is studied for different N leading to the conclusion that the chiral fixed point governing the critical behavior of physical systems with N = 2 and N = 3 does not coincide with that given by the 1/N expansion. We show that the stable chiral fixed point for $N \le N^*$, including N = 2 and N = 3, turns out to be a focus. We give a complete characterization of the critical behavior controlled by this fixed point, also evaluating the subleading crossover exponents. The spiral-like approach of the chiral fixed point is argued to give rise to unusual crossover and near-critical regimes that may imitate varying critical exponents seen in numerous physical and computer experiments.Comment: 17 pages, 12 figure

Critical thermodynamics of three-dimensional chiral model for N > 3

The critical behavior of the three-dimensional $N$-vector chiral model is studied for arbitrary $N$. The known six-loop renormalization-group (RG) expansions are resummed using the Borel transformation combined with the conformal mapping and Pad\'e approximant techniques. Analyzing the fixed point location and the structure of RG flows, it is found that two marginal values of $N$ exist which separate domains of continuous chiral phase transitions $N > N_{c1}$ and $N N > N_{c2}$ where such transitions are first-order. Our calculations yield $N_{c1} = 6.4(4)$ and $N_{c2} = 5.7(3)$. For $N > N_{c1}$ the structure of RG flows is identical to that given by the $\epsilon$ and 1/N expansions with the chiral fixed point being a stable node. For $N < N_{c2}$ the chiral fixed point turns out to be a focus having no generic relation to the stable fixed point seen at small $\epsilon$ and large $N$. In this domain, containing the physical values $N = 2$ and $N = 3$, phase trajectories approach the fixed point in a spiral-like manner giving rise to unusual crossover regimes which may imitate varying (scattered) critical exponents seen in numerous physical and computer experiments.Comment: 12 pages, 3 figure