The response of the worldwide scientific community to the discovery in 2008 of superconductivity at Tc = 26 K in the Fe-based compound LaFeAsO1−xFx has been very enthusiastic. In short order, other Fe-based superconductors with the same or related crystal structures were discovered with Tc up to 56 K. Many experiments were carried out and theories formulated to try to understand the basic properties of these new materials and the mechanism for Tc. In this selective critical review of the experimental literature, we distill some of this extensive body of work, and discuss relationships between different types of experiments on these materials with reference to theoretical concepts and models. The experimental normal-state properties are emphasized, and within these the electronic and magnetic properties because of the likelihood of an electronic/magnetic mechanism for superconductivity in these materials. Contents

The magnetic susceptibility *(t) and specific heat C(t) versus temperature t of the spin Sϭ1/2 antiferromagnetic ͑AF͒ alternating-exchange (J 1 and J 2 ) Heisenberg chain are studied for the entire range 0р␣р1 of the alternation parameter ␣ϵJ ). For the uniform chain (␣ϭ1), the high-accuracy *(t) and C(t) Bethe ansatz data of Klümper and Johnston ͑unpublished͒ are shown to agree very well at low t with the respective exact theoretical low-t logarithmic correction predictions of Lukyanov ͓Nucl. Phys. B 522, 533 ͑1998͔͒. Accurate (ϳ10 Ϫ7 ) independent empirical fits to the respective data are obtained over t ranges spanning 25 orders of magnitude, 5ϫ10 Ϫ25 рtр5, which contain extrapolations to the respective exact tϭ0 limits. The infinite temperature entropy calculated using our C(t) fit function is within 8 parts in 10 8 of the exact value ln 2. Quantum Monte Carlo ͑QMC͒ simulations and transfer-matrix density-matrix renormalization group ͑TMRG͒ calculations of *(␣,t) are presented for 0.002рtр10 and 0.05р␣р1, and an accurate (2ϫ10 Ϫ4 ) two-dimensional (␣,t) fit to the combined data is obtained for 0.01 рtр10 and 0р␣р1. From the low-t TMRG data, the spin gap ⌬(␣) is extracted for 0.8р␣р0.995 and compared with previous results, and a fit function is formulated for 0р␣р1 by combining these data with literature data. We infer from our data that the asymptotic critical regime near the uniform chain limit is only entered for ␣տ0.99. We examine in detail the theoretical predictions of Bulaevskii ͓Sov. Phys. Solid State 11, 921 ͑1969͔͒, for *(␣,t) and compare them with our results. To illustrate the application and utility of our theoretical results, we model our experimental (T) and specific heat C p (T) data for NaV 2 O 5 single crystals in detail. The (T) data above the spin dimerization temperature T c Ϸ34 K are not in quantitative agreement with the prediction for the Sϭ1/2 uniform Heisenberg chain, but can be explained if there is a moderate ferromagnetic interchain coupling and/or if J changes with T. Fitting the (T) data using our *(␣,t) fit function, we obtain the sample-dependent spin gap and range ⌬(Tϭ0)/k B ϭ103(2) K, alternation parameter ␦(0)ϵ(1Ϫ␣)/(1ϩ␣)ϭ0.034(6) and average exchange constant J(0)/k B ϭ640(80) K. The ␦(T) and ⌬(T) are derived from the data. A spin pseudogap with magnitude Ϸ0.4⌬(0) is consistently found just above T c , which decreases with increasing temperature. From our C p (T) measurements on two crystals, we infer that the magnetic specific heat at low temperatures TՇ15 K is too small to be resolved experimentally, and that the spin entropy at T c is too small to account for the entropy of the transition. A quantitative analysis indicates that at T c , at least 77% of the entropy change due to the transition at T c and associated order parameter fluctuations arise from the lattice and/or charge degrees of freedom and less than 23% from the spin degrees of freedom.

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Stretched exponential relaxation of a quantity n versus time t according to n = n 0 exp͓−͑ * t͒ ␤ ͔ is ubiquitous in many research fields, where * is a characteristic relaxation rate and the stretching exponent ␤ is in the range 0 Ͻ ␤ Ͻ 1. Here we consider systems in which stretched exponential relaxation arises from global relaxation of a system containing independently exponentially relaxing species with a probability distribution P͑ / * , ␤͒ of relaxation rates . We study the properties of P͑ / * , ␤͒ and their dependence on ␤. Physical interpretations of * and ␤, derived from consideration of P͑ / * , ␤͒ and its moments, are discussed.

Predictions of the anisotropic magnetic susceptibility χ below the antiferromagnetic (AFM) ordering temperatures TN of local moment Heisenberg AFMs have been made previously using molecular field theory (MFT) but are very limited in their applicability. Here a MFT calculation of χ(T ≤ TN) is presented for a wide variety of collinear and noncollinear Heisenberg AFMs containing identical crystallographically equivalent spins without recourse to magnetic sublattices. The results are expressed in terms of directly measurable experimental parameters and are fitted with no adjustable parameters to experimental χ(T ≤ TN) data from the literature for several collinear and noncollinear AFMs. The influence of spin correlations and fluctuations beyond MFT is quantified by the deviation of the theory from the data. The origin of the universal χ(T ≤ TN) observed for triangular lattice AFMs exhibiting coplanar noncollinear 120• AFM ordering is clarified.Introduction. Magnetic susceptibility χ measurements versus temperature T have been used for a century to obtain important information about the magnetic properties of materials. The Weiss molecular field theory (MFT) has been instrumental in interpreting the χ(T ) data in the paramagnetic state above the long-range magnetic ordering temperature T N of local magnetic moment antiferromagnets 1,2 (AFMs) via the Curie-Weiss (CW) law χ =