The high temperature expansion of the classical XYZXYZ chain

We present the $\beta$-expansion of the Helmholtz free energy of the classical $XYZ$ model, with a single-ion anisotropy term and in the presence of an external magnetic field, up to order $\beta^{12}$. We compare our results to the numerical solution of Joyce's [Phys. Rev. Lett. 19, 581 (1967)] expression for the thermodynamics of the $XXZ$ classical model, with neither single-ion anisotropy term nor external magnetic field. This comparison shows that the derived analytical expansion is valid for intermediate temperatures such as $kT/J_x \approx 0.5$. We show that the specific heat and magnetic susceptibility of the spin-2 antiferromagnetic chain can be approximated by their respective classical results, up to $kT/J \approx 0.8$, within an error of 2.5%. In the absence of an external magnetic field, the ferromagnetic and antiferromagnetic chains have the same classical Helmholtz free energy. We show how this two types of media react to the presence of an external magnetic field

Relativistic Quark Spin Coupling Effects in the Correlations Between Nucleon Electroweak Properties

We investigate the effect of different relativistic spin couplings of constituent quarks on nucleon electroweak properties. Within each quark spin coupling scheme the correlations between static electroweak observables are found to be independent of the particular shape of the momentum part of the nucleon light-front wave function. The neutron charge form factor is very sensitive to different choices of spin coupling schemes once the magnetic moment is fitted to the experimental value. However, it is found rather insensitive to the details of the momentum part of the three-quark wave function model.Comment: 23 pages, 13 figures, requires axodraw.sty 1 figure corrected, 1 refs. added, some changes in tex

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Charged pion form factor between Q^2=0.60 and 2.45 GeV^2. II. Determination of, and results for, the pion form factor

The charged pion form factor, Fpi(Q^2), is an important quantity which can be used to advance our knowledge of hadronic structure. However, the extraction of Fpi from data requires a model of the 1H(e,e'pi+)n reaction, and thus is inherently model dependent. Therefore, a detailed description of the extraction of the charged pion form factor from electroproduction data obtained recently at Jefferson Lab is presented, with particular focus given to the dominant uncertainties in this procedure. Results for Fpi are presented for Q^2=0.60-2.45 GeV^2. Above Q^2=1.5 GeV^2, the Fpi values are systematically below the monopole parameterization that describes the low Q^2 data used to determine the pion charge radius. The pion form factor can be calculated in a wide variety of theoretical approaches, and the experimental results are compared to a number of calculations. This comparison is helpful in understanding the role of soft versus hard contributions to hadronic structure in the intermediate Q^2 regime.Comment: 18 pages, 11 figure

A re-interpretation of the concept of mass and of the relativistic mass-energy relation

For over a century the definitions of mass and derivations of its relation with energy continue to be elaborated, demonstrating that the concept of mass is still not satisfactorily understood. The aim of this study is to show that, starting from the properties of Minkowski spacetime and from the principle of least action, energy expresses the property of inertia of a body. This implies that inertial mass can only be the object of a definition - the so called mass-energy relation - aimed at measuring energy in different units, more suitable to describe the huge amount of it enclosed in what we call the "rest-energy" of a body. Likewise, the concept of gravitational mass becomes unnecessary, being replaceable by energy, thus making the weak equivalence principle intrinsically verified. In dealing with mass, a new unit of measurement is foretold for it, which relies on the de Broglie frequency of atoms, the value of which can today be measured with an accuracy of a few parts in 10^9

Active Brownian Particles. From Individual to Collective Stochastic Dynamics

We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework of statistical mechanics. Examples of such active units in complex physico-chemical and biological systems are chemically powered nano-rods, localized patterns in reaction-diffusion system, motile cells or macroscopic animals. Based on the description of individual motion of point-like active particles by stochastic differential equations, we discuss different velocity-dependent friction functions, the impact of various types of fluctuations and calculate characteristic observables such as stationary velocity distributions or diffusion coefficients. Finally, we consider not only the free and confined individual active dynamics but also different types of interaction between active particles. The resulting collective dynamical behavior of large assemblies and aggregates of active units is discussed and an overview over some recent results on spatiotemporal pattern formation in such systems is given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte

Diverse Beliefs and Time Variability of Risk Premia

Why do risk premia vary over time? We examine this problem theoretically and empirically by studying the effect of market belief on risk premia. Individual belief is taken as a fundamental primitive state variable. Market belief is observable; it is central to the empirical evaluation and we show how to measure it. Our asset pricing model is familiar from the noisy REE literature but we adapt it to an economy with diverse beliefs. We derive equilibrium asset prices and implied risk premium. Our approach permits a closed form solution of prices; hence we trace the exact effect of market belief on the time variability of asset prices and risk premia. We test empirically the theoretical conclusions. Our main result is that, above the effect of business cycles on risk premia, fluctuations in market belief have significant independent effect on the time variability of risk premia. We study the premia on long positions in Federal Funds Futures, 3- and 6-month Treasury Bills (T-Bills). The annual mean risk premium on holding such assets for 1-12 months is about 40-60 basis points and we find that, on average, the component of market belief in the risk premium exceeds 50% of the mean. Since time variability of market belief is large, this component frequently exceeds 50% of the mean premium. This component is larger the shorter is the holding period of an asset and it dominates the premium for very short holding returns of less than 2 months. As to the structure of the premium we show that when the market holds abnormally favorable belief about the future payoff of an asset the market views the long position as less risky hence the risk premium on that asset declines. More generally, periods of market optimism (i.e. "bull" markets) are shown to be periods when the market risk premium is low while in periods of pessimism (i.e. "bear" markets) the market's risk premium is high. Fluctuations in risk premia are thus inversely related to the degree of market optimism about future prospects of asset payoffs. This effect is strong and economically very significant