The Imago Primi Saeculi Societatis Iesv (1640). Devotion, Politics and the Emblem.

The Imago Primi Saeculi Societatis Iesv (1640) is, perhaps, the most beautiful book of emblems published by the Jesuits in the seventeenth century. The book is a festive commemoration offered by the priests and students of the Flemish-Belgian Province in celebration of the centenary of the founding of the Society of Jesus. The work includes 127 full-page emblems distributed throughout a total of 956 folio-sized pages that narrate and illustrate in emblematic fashion the foundation, development, vicisstitudes and achievements of the Socirty in its evangelical and pedagogical mission. From the moment of its publication, the Imago was the object of attacks by Huguenauts and Jansenists who criticized its haughtiness, grandiloquent language and the hyperbolic comparisons of the narration. Hidden behind this criticism were the reasons for the Jansenist offensive against the book. Probabilism, the supposed frivolous attitude towards confession and the frequency of communion, advocated by the Jesuits, was the object of a pair of insulting treatises directed against the Imago by the famous Jansenists Antoine Arnauld and Issac Louis le Maître de Sacy. The critics of the Imago maliciously ignored that the book's grandiloquent style, appropriate to a jubilation celebration, conforms to the language of classical rhetoric, thus perpetuating the propagandistic image of the book. KEYWORDS: Imago Primi Saeculi; Society of Jesus; Flanders; Flemish-Belgian Province

Enhancement of magnetic anisotropy barrier in long range interacting spin systems

Magnetic materials are usually characterized by anisotropy energy barriers which dictate the time scale of the magnetization decay and consequently the magnetic stability of the sample. Here we present a unified description, which includes coherent rotation and nucleation, for the magnetization decay in generic anisotropic spin systems. In particular, we show that, in presence of long range exchange interaction, the anisotropy energy barrier grows as the volume of the particle for on site anisotropy, while it grows even faster than the volume for exchange anisotropy, with an anisotropy energy barrier proportional to $V^{2-\alpha/d}$, where $V$ is the particle volume, $\alpha \leq d$ is the range of interaction and $d$ is the embedding dimension. These results shows a relevant enhancement of the anisotropy energy barrier w.r.t. the short range case, where the anisotropy energy barrier grows as the particle cross sectional area for large particle size or large particle aspect ratio.Comment: 7 pages, 6 figures. Theory of Magnetic decay in nanosystem. Non equilibrium statistical mechanics of many body system

Microcanonical Analysis of Exactness of the Mean-Field Theory in Long-Range Interacting Systems

Classical spin systems with nonadditive long-range interactions are studied in the microcanonical ensemble. It is expected that the entropy of such a system is identical to that of the corresponding mean-field model, which is called "exactness of the mean-field theory". It is found out that this expectation is not necessarily true if the microcanonical ensemble is not equivalent to the canonical ensemble in the mean-field model. Moreover, necessary and sufficient conditions for exactness of the mean-field theory are obtained. These conditions are investigated for two concrete models, the \alpha-Potts model with annealed vacancies and the \alpha-Potts model with invisible states.Comment: 23 pages, to appear in J. Stat. Phy

Canonical solution of a system of long-range interacting rotators on a lattice

The canonical partition function of a system of rotators (classical X-Y spins) on a lattice, coupled by terms decaying as the inverse of their distance to the power alpha, is analytically computed. It is also shown how to compute a rescaling function that allows to reduce the model, for any d-dimensional lattice and for any alpha<d, to the mean field (alpha=0) model.Comment: Initially submitted to Physical Review Letters: following referees' Comments it has been transferred to Phys. Rev. E, because of supposed no general interest. Divided into sections, corrections in (5) and (20), reference 5 updated. 8 pages 1 figur

Canonical Solution of Classical Magnetic Models with Long-Range Couplings

We study the canonical solution of a family of classical $n-vector$ spin models on a generic $d$-dimensional lattice; the couplings between two spins decay as the inverse of their distance raised to the power $\alpha$, with $\alpha<d$. The control of the thermodynamic limit requires the introduction of a rescaling factor in the potential energy, which makes the model extensive but not additive. A detailed analysis of the asymptotic spectral properties of the matrix of couplings was necessary to justify the saddle point method applied to the integration of functions depending on a diverging number of variables. The properties of a class of functions related to the modified Bessel functions had to be investigated. For given $n$, and for any $\alpha$, $d$ and lattice geometry, the solution is equivalent to that of the $\alpha=0$ model, where the dimensionality $d$ and the geometry of the lattice are irrelevant.Comment: Submitted for publication in Journal of Statistical Physic

1-d gravity in infinite point distributions

The dynamics of infinite, asymptotically uniform, distributions of self-gravitating particles in one spatial dimension provides a simple toy model for the analogous three dimensional problem. We focus here on a limitation of such models as treated so far in the literature: the force, as it has been specified, is well defined in infinite point distributions only if there is a centre of symmetry (i.e. the definition requires explicitly the breaking of statistical translational invariance). The problem arises because naive background subtraction (due to expansion, or by "Jeans' swindle" for the static case), applied as in three dimensions, leaves an unregulated contribution to the force due to surface mass fluctuations. Following a discussion by Kiessling, we show that the problem may be resolved by defining the force in infinite point distributions as the limit of an exponentially screened pair interaction. We show that this prescription gives a well defined (finite) force acting on particles in a class of perturbed infinite lattices, which are the point processes relevant to cosmological N-body simulations. For identical particles the dynamics of the simplest toy model is equivalent to that of an infinite set of points with inverted harmonic oscillator potentials which bounce elastically when they collide. We discuss previous results in the literature, and present new results for the specific case of this simplest (static) model starting from "shuffled lattice" initial conditions. These show qualitative properties (notably its "self-similarity") of the evolution very similar to those in the analogous simulations in three dimensions, which in turn resemble those in the expanding universe.Comment: 20 pages, 8 figures, small changes (section II shortened, added discussion in section IV), matches final version to appear in PR

An Options-Based Analysis of Emerging Market Exchange Rate Expectations: Brazil's Real Plan, 1994-1997

This paper uses currency option data from the BMF, the Commodities and Futures exchange in Sao Paulo, Brazil, to investigate market expectations on the Brazilian Real-U.S. dollar exchange rate from October 1994 through July 1997. Using options data, we derive implied probability density functions (PDF) for expected future exchange rates and thus measures of the credibility of the “crawling peg” and target zone (“maxiband”) regimes governing the exchange rate. Since we do not impose an exchange rate model, our analysis is based on either the risk-neutral PDF or arbitrage-based tests of target zones. The paper, one of the first to use options data from an emerging market, finds that target zone credibility was poor prior to February 1996, but improved afterwards. The market anticipated periodic band adjustments, but over time developed greater confidence in the Real. We also test whether devaluation intensities estimated from these option prices can be explained by standard macroeconomic factors

Dynamical stability criterion for inhomogeneous quasi-stationary states in long-range systems

We derive a necessary and sufficient condition of linear dynamical stability for inhomogeneous Vlasov stationary states of the Hamiltonian Mean Field (HMF) model. The condition is expressed by an explicit disequality that has to be satisfied by the stationary state, and it generalizes the known disequality for homogeneous stationary states. In addition, we derive analogous disequalities that express necessary and sufficient conditions of formal stability for the stationary states. Their usefulness, from the point of view of linear dynamical stability, is that they are simpler, although they provide only sufficient criteria of linear stability. We show that for homogeneous stationary states the relations become equal, and therefore linear dynamical stability and formal stability become equivalent.Comment: Submitted to Journal of Statistical Mechanics: Theory and Experimen

Relaxation to thermal equilibrium in the self-gravitating sheet model

We revisit the issue of relaxation to thermal equilibrium in the so-called "sheet model", i.e., particles in one dimension interacting by attractive forces independent of their separation. We show that this relaxation may be very clearly detected and characterized by following the evolution of order parameters defined by appropriately normalized moments of the phase space distribution which probe its entanglement in space and velocity coordinates. For a class of quasi-stationary states which result from the violent relaxation of rectangular waterbag initial conditions, characterized by their virial ratio R_0, we show that relaxation occurs on a time scale which (i) scales approximately linearly in the particle number N, and (ii) shows also a strong dependence on R_0, with quasi-stationary states from colder initial conditions relaxing much more rapidly. The temporal evolution of the order parameter may be well described by a stretched exponential function. We study finally the correlation of the relaxation times with the amplitude of fluctuations in the relaxing quasi-stationary states, as well as the relation between temporal and ensemble averages.Comment: 37 pages, 24 figures; some additional discussion of previous literature and other minor modifications, final published versio