The ideal glass transition of Hard Spheres

We use the replica method to study the ideal glass transition of a liquid of identical Hard Spheres. We obtain estimates of the configurational entropy in the liquid phase, of the Kauzmann packing fraction, in the range 0.58--0.62, and of the random close packing density, in the range 0.64--0.67, depending on the approximation we use for the equation of state of the liquid. We also compute the pair correlation function in the glassy states (i.e., dense amorphous packings) and we find that the mean coordination number at random close packing is equal to 6. All these results compare well with numerical simulations and with other existing theories.Comment: 13 pages, 8 figure

Amorphous packings of hard spheres in large space dimension

In a recent paper (cond-mat/0506445) we derived an expression for the replicated free energy of a liquid of hard spheres based on the HNC free energy functional. An approximate equation of state for the glass and an estimate of the random close packing density were obtained in d=3. Here we show that the HNC approximation is not needed: the same expression can be obtained from the full diagrammatic expansion of the replicated free energy. Then, we consider the asymptotics of this expression when the space dimension d is very large. In this limit, the entropy of the hard sphere liquid has been computed exactly. Using this solution, we derive asymptotic expressions for the glass transition density and for the random close packing density for hard spheres in large space dimension.Comment: 11 pages, 1 figure, includes feynmf diagram

Replica Field Theory for Deterministic Models: Binary Sequences with Low Autocorrelation

We study systems without quenched disorder with a complex landscape, and we use replica symmetry theory to describe them. We discuss the Golay-Bernasconi-Derrida approximation of the low autocorrelation model, and we reconstruct it by using replica calculations. Then we consider the full model, its low $T$ properties (with the help of number theory) and a Hartree-Fock resummation of the high-temperature series. We show that replica theory allows to solve the model in the high $T$ phase. Our solution is based on one-link integral techniques, and is based on substituting a Fourier transform with a generic unitary transformation. We discuss this approach as a powerful tool to describe systems with a complex landscape in the absence of quenched disorder.Comment: 42 pages, uufile with eps figures added in figures, ROM2F/94/1

Spin-1 gravitational waves. Theoretical and experimental aspects

Exact solutions of Einstein field equations invariant for a non-Abelian 2-dimensional Lie algebra of Killing fields are described. Physical properties of these gravitational fields are studied, their wave character is checked by making use of covariant criteria and the observable effects of such waves are outlined. The possibility of detection of these waves with modern detectors, spherical resonant antennas in particular, is sketched

Fragility in p-spin models

We investigate the relation between fragility and phase space properties - such as the distribution of states - in the mean field p-spin model, a solvable model that has been frequently used in studies of the glass transition. By direct computation of all the relevant quantities, we find that: i) the recently observed correlation between fragility and vibrational properties at low temperature is present in this model; ii) the total number of states is a decreasing function of fragility, at variance of what is currently believed. We explain these findings by taking into account the contribution to fragility coming from the transition paths between different states. Finally, we propose a geometric picture of the phase space that explains the correlation between properties of the transition paths, distribution of states and their vibrational properties. However, our analysis may not apply to strong systems where inflection points in the configurational entropy as a function of the temperature are found

A note on rattlers in amorphous packings of binary mixtures of hard spheres

It has been recently pointed out by Farr and Groot (arXiv:0912.0852) and by Kyrylyuk and Philipse (Prog. Colloid Polym. Sci., 2010, in press) that our theoretical result for the jamming density of a binary mixture of hard spheres (arXiv:0903.5099) apparently violates an upper bound that is obtained by considering the limit where the diameter ratio r = DA/DB goes to infinity. We believe that this apparent contradiction is the consequence of a misunderstanding, which we try to clarify here.Comment: 2 pages, 2 figures; final version published on J.Chem.Phy

On the Use of Optimized Monte Carlo Methods for Studying Spin Glasses

We start from recently published numerical data by Hatano and Gubernatis cond-mat/0008115 to discuss properties of convergence to equilibrium of optimized Monte Carlo methods (bivariate multi canonical and parallel tempering). We show that these data are not thermalized, and they lead to an erroneous physical picture. We shed some light on why the bivariate multi canonical Monte Carlo method can fail.Comment: 6 pages, 5 eps figures include

Assessment of ultraviolet radiation exposures in photobiological experiments

The interfering effect of ultraviolet (UV) radiation on the natural function of biological processes is wavelength specific and the UV spectrum must be weighted with the action spectrum for the process. The UV spectral irradiance may be measured with calibrated spectroradiometers. Alternatively, the biologically effective UV may be measured with broadband devices. This paper reviews the techniques for assessing biologically effective exposures in photobiological experiments. UV meters, such as the Robertson-Berger (RB) meter, or passive dosimeters, such as polysulphone, that possess a spectral response approximating the human erythemal response can be used to estimate erythemally effective exposure or actinic exposure due to solar UV. The sensitivity of the RB meter is about 0.56 uW cm-2 and polysulphone can record an exposure of about 2mJ cm-2. For photobiological processes other than erythema these devices are not suitable to determine the exposure. In terms of these applications, a spectrum evaluator consisting of four different types of dosimeter material can be employed to evaluate the UV spectrum of the source. This method can be useful both for solar UV studies and research with UV lamps that possess radiation wavelengths shorter than 295nm. The device can be used to measure exposures where the actinic and erythemal action spectra differ significantly. It can also be used to assess exposure due to low levels of UV (about 0.01uW cm-2) caused by radiation filtered through glasses or plastic

Explicit generation of the branching tree of states in spin glasses

We present a numerical method to generate explicit realizations of the tree of states in mean-field spin glasses. The resulting study illuminates the physical meaning of the full replica symmetry breaking solution and provides detailed information on the structure of the spin-glass phase. A cavity approach ensures that the method is self-consistent and permits the evaluation of sophisticated observables, such as correlation functions. We include an example application to the study of finite-size effects in single-sample overlap probability distributions, a topic that has attracted considerable interest recently.Comment: Version accepted for publication in JSTA