Existence of a Thermodynamic Spin-Glass Phase in the Zero-Concentration Limit of Anisotropic Dipolar Systems

The nature of ordering in dilute dipolar interacting systems dates back to the work of Debye and is one of the most basic, oldest and as-of-yet unsettled problems in magnetism. While spin-glass order is readily observed in several RKKY-interacting systems, dipolar spin-glasses are subject of controversy and ongoing scrutiny, e.g., in ${{\rm LiHo_xY_{1-x}F_4}}$, a rare-earth randomly diluted uniaxial (Ising) dipolar system. In particular, it is unclear if the spin-glass phase in these paradigmatic materials persists in the limit of zero concentration or not. We study an effective model of ${{\rm LiHo_xY_{1-x}F_4}}$ using large-scale Monte Carlo simulations that combine parallel tempering with a special cluster algorithm tailored to overcome the numerical difficulties that occur at extreme dilutions. We find a paramagnetic to spin-glass phase transition for all Ho ion concentrations down to the smallest concentration numerically accessible of 0.1%, and including Ho ion concentrations which coincide with those studied experimentally up to 16.7%. Our results suggest that randomly-diluted dipolar Ising systems have a spin-glass phase in the limit of vanishing dipole concentration, with a critical temperature vanishing linearly with concentration, in agreement with mean field theory.Comment: 6 pages, 3 figures, 2 table

Characterization of gamma-ray burst prompt emission spectra down to soft X-rays

Detection of prompt emission by Swift-XRT provides a unique tool to study how the prompt spectrum of gamma-ray bursts (GRBs) extends down to the soft X-ray band. This energy band is particularly important for prompt emission studies, since it is towards low energies that the observed spectral shape is in disagreement with the synchrotron predictions. Unfortunately, the number of cases where XRT started observing the GRB location during the prompt phase is very limited. In this work, we collect a sample of 34 GRBs and perform joint XRT+BAT spectral analysis of prompt radiation, extending a previous study focused on the 14 brightest cases. Fermi-GBM observations are included in the analysis when available (11 cases), allowing the characterization of prompt spectra from soft X-rays to MeV energies. In 62% of the spectra, the XRT data reveal a hardening of the spectrum, well described by introducing an additional, low-energy power-law segment (with index \u3b1 1 ) into the empirical fitting function. The break energy below which the spectrum hardens has values between 3 keV and 22 keV. A second power-law (\u3b1 2 ) describes the spectrum between the break energy and the peak energy. The mean values of the photon indices are (\u3b1 1 ) = -0.51 (\u3c3 = 0.24) and (\u3b1 2 ) = -1.56 (\u3c3 = 0.26). These are consistent, within one \u3c3, with the synchrotron values in fast cooling regime. As a test, if we exclude XRT data from the fits we find typical results: the spectrum below the peak energy is described by a power law with (\u3b1) = -1.15. This shows the relevance of soft X-ray data in revealing prompt emission spectra consistent with synchrotron spectra. Finally, we do not find any correlation between the presence of the X-ray break energy and the flux, fluence, or duration of the prompt emission

Price formation mechanism and tariff protection in a dynamic model of a small open economy in transition

This paper examines the importance and dynamics of prices in a small open economy in transition. Several main features of this process outline the behavior of the mathematical model. The model examines four factors that affect prices after the liberalization of the domestic market: the domestic producer price, the cost price of inefficiency, the hyperinflation price, and the world market price, which includes the dynamics of the exchange rate. The numeric simulation of the price dynamics for the cheese segment of Ukrainian food market was made.Досліджено основні процеси, що впливають на динаміку цін у невеликій відкритій перехідній економіці. Розглянуто декілька характерних особливостей такої економіки, що визначають поведінку математичної моделі. У моделі враховано чотири фактори, що впливають на ціноутворення після лібералізації внутрішнього ринку: ціна внутрішнього виробника, ціна неефективності виробництва, гіперінфляційна ціна та ціна на світовому ринку, яка, в свою чергу, враховує динаміку валютного курсу. Представлено результати чисельного моделювання динаміки цін в одному з сегментів ринку продовольчих товарів на Україні, а саме, ринку твердих сирів.Исследованы основные процессы, влияющие на динамику цен в небольшой открытой переходной экономике. Рассмотрено несколько отличительных особенностей такой экономики, определяющих поведение математической модели. В модели учтены четыре фактора, которые влияют на ценообразование после либерализации внутреннего рынка: цена внутреннего производителя, цена неэффективности производства, гиперинфляционная цена и цена на мировом рынке, которая, в свою очередь, учитывает динамику валютного курса. Представлены результаты многочисленного моделирования динамики цен в одном из сегментов рынка продовольственных товаров в Украине, а именно, рынка твердых сыров

Prompt optical emission as a signature of synchrotron radiation in gamma-ray bursts

Information on the spectral shape of prompt emission in gamma-ray bursts (GRB) is mostly available only at energies greater than or similar to 10 keV, where the main instruments for GRB detection are sensitive. The origin of this emission is still very uncertain because of the apparent inconsistency with synchrotron radiation, which is the most obvious candidate, and the resulting need for considering less straight-forward scenarios. The inclusion of data down to soft X-rays (similar to 0.5 keV), which are available only in a small fraction of GRBs, has firmly established the common presence of a spectral break in the low-energy part of prompt spectra, and even more importantly, the consistency of the overall spectral shape with synchrotron radiation in the moderately fast-cooling regime, the low-energy break being identified with the cooling frequency. In this work we further extend the range of investigation down to the optical band. In particular, we test the synchrotron interpretation by directly fitting a theoretically derived synchrotron spectrum and making use of optical to gamma-ray data. Secondly, we test an alternative model that considers the presence of a black-body component at similar to keV energies, in addition to a non-thermal component that is responsible for the emission at the spectral peak (100 keV-1 MeV). We find that synchrotron radiation provides a good description of the broadband data, while models composed of a thermal and a non-thermal component require the introduction of a low-energy break in the non-thermal component in order to be consistent with optical observations. Motivated by the good quality of the synchrotron fits, we explore the physical parameter space of the emitting region. In a basic prompt emission scenario we find quite contrived solutions for the magnetic field strength (5G < B' < 40 G) and for the location of the region where the radiation is produced (R-gamma > 10(16) cm). We discuss which assumptions of the basic model would need to be relaxed in order to achieve a more natural parameter space