Multi-species mean-field spin-glasses. Rigorous results

We study a multi-species spin glass system where the density of each species is kept fixed at increasing volumes. The model reduces to the Sherrington-Kirkpatrick one for the single species case. The existence of the thermodynamic limit is proved for all densities values under a convexity condition on the interaction. The thermodynamic properties of the model are investigated and the annealed, the replica symmetric and the replica symmetry breaking bounds are proved using Guerra's scheme. The annealed approximation is proved to be exact under a high temperature condition. We show that the replica symmetric solution has negative entropy at low temperatures. We study the properties of a suitably defined replica symmetry breaking solution and we optimise it within a ziggurat ansatz. The generalized order parameter is described by a Parisi-like partial differential equation.Comment: 17 pages, to appear in Annales Henri Poincar\`

Quasi-Static Brittle Fracture in Inhomogeneous Media and Iterated Conformal Maps: Modes I, II and III

The method of iterated conformal maps is developed for quasi-static fracture of brittle materials, for all modes of fracture. Previous theory, that was relevant for mode III only, is extended here to mode I and II. The latter require solution of the bi-Laplace rather than the Laplace equation. For all cases we can consider quenched randomness in the brittle material itself, as well as randomness in the succession of fracture events. While mode III calls for the advance (in time) of one analytic function, mode I and II call for the advance of two analytic functions. This fundamental difference creates different stress distribution around the cracks. As a result the geometric characteristics of the cracks differ, putting mode III in a different class compared to modes I and II.Comment: submitted to PRE For a version with qualitatively better figures see: http://www.weizmann.ac.il/chemphys/ander

Molecular Solvation in Phosphonium Ionic Liquids

The goal of this research is to understand the solvation dynamics of coumarin 153 (C153) in an environmentally-friendly room temperature phosphonium ionic liquid (RTPIL) solvent. With virtually no vapor pressure, ILs are attracting attention as potential “green” replacements for conventional volatile organic solvents. ILs are also known for chemical stability, non-flammability and recycling potential. C153 is a prototypical fluorescent molecule known for its spectral sensitivity when in solution making it ideal for these studies. Neat trihexyltetradecyl phosphonium chloride (PIL-Cl) and methanol (MeOH) solvents were used to form an array of PIL-Cl mixtures spanning the complete range of mol fraction, in which C153 was dissolved. Solvation of C153 was determined using steady-state and time-resolved fluorescence spectroscopy. The C153 steady-state data shows a systematic blue shift as PIL-Cl is added to solution. The system is at net higher energy at high mol fraction PIL-Cl implying that C153/PIL-Cl interactions are less favorable compared to C153/MeOH. The solute emission intensity is quenched most effectively at a mol fraction of ~0.03 PIL-Cl suggesting that the solvent-solute interactions are most unique in this range of mol fraction. Similarly, the lifetime data show a minimum value at ~0.03 mol fraction PIL-Cl, also implying quenching of the probe at this relative solution composition. C153 is better solvated, more relaxed, at MeOH-rich mol fractions. Solvation dynamics are characterized by time-resolved Stokes shift measurements. The time-resolved center of gravity and associated solvation correlation function, C(t), show that solvation of C153 occurs at a faster rate in solutions of lower mol fraction PIL-Cl. The solvation times correlate to solvent viscosity. PILs showed slower solvation due to much larger viscosities than MeOH

The Rise of The Short Story In American Letters

Like all other nations America too has had her birth in the literally world. Her beginning has not been less forceful than other nations. We find that English literature, undivided in the past, at the end of the nineteenth century has four divisions: British, American, Canadian, and Australian. The British is still the most important since it has the greatest literary background. But the steadily growing American literature ranks second to it. We glory in this heritage as much as the British because we feel that it belongs to us as well, and prize this tremendous possessio

Interpolating the Sherrington-Kirkpatrick replica trick

The interpolation techniques have become, in the past decades, a powerful approach to lighten several properties of spin glasses within a simple mathematical framework. Intrinsically, for their construction, these schemes were naturally implemented into the cavity field technique, or its variants as the stochastic stability or the random overlap structures. However the first and most famous approach to mean field statistical mechanics with quenched disorder is the replica trick. Among the models where these methods have been used (namely, dealing with frustration and complexity), probably the best known is the Sherrington-Kirkpatrick spin glass: In this paper we are pleased to apply the interpolation scheme to the replica trick framework and test it directly to the cited paradigmatic model: interestingly this allows to obtain easily the replica-symmetric control and, synergically with the broken replica bounds, a description of the full RSB scenario, both coupled with several minor theorems. Furthermore, by treating the amount of replicas $n\in(0,1]$ as an interpolating parameter (far from its original interpretation) this can be though of as a quenching temperature close to the one introduce in off-equilibrium approaches and, within this viewpoint, the proof of the attended commutativity of the zero replica and the infinite volume limits can be obtained.Comment: This article is dedicated to David Sherrington on the occasion of his seventieth birthda

KETERBACAAN ANALISIS DAN DISKUSI MANAJEMEN DALAM LAPORAN TAHUNAN (Studi Empiris Pada Perusahaan Manufaktur Yang Terdaftar Di Bursa Efek Indonesia Tahun 2014)

MD&A is the important part in the annual report, as it speaks to all stakeholders about companies performance and future plans, it should be readable and comprehensible. The main objective of this study is to determine the readability of MD&A from manufacture companies in Indonesia. The population in this study consist of all manufacture companies listed firms in Indonesia Stock Exchange in year 2014. Sampling method used is simple random sampling. A total sample of 107 companies were used in this analysis. The data is analyzed using readability index and statistic descriptive analysis. The empirical results of this study show that the MD&A are difficult to read and comprehend, it require 12,080 years of formal education before they can fully understood

The replica symmetric behavior of the analogical neural network

In this paper we continue our investigation of the analogical neural network, paying interest to its replica symmetric behavior in the absence of external fields of any type. Bridging the neural network to a bipartite spin-glass, we introduce and apply a new interpolation scheme to its free energy that naturally extends the interpolation via cavity fields or stochastic perturbations to these models. As a result we obtain the free energy of the system as a sum rule, which, at least at the replica symmetric level, can be solved exactly. As a next step we study its related self-consistent equations for the order parameters and their rescaled fluctuations, found to diverge on the same critical line of the standard Amit-Gutfreund-Sompolinsky theory.Comment: 17 page

Criticality in diluted ferromagnet

We perform a detailed study of the critical behavior of the mean field diluted Ising ferromagnet by analytical and numerical tools. We obtain self-averaging for the magnetization and write down an expansion for the free energy close to the critical line. The scaling of the magnetization is also rigorously obtained and compared with extensive Monte Carlo simulations. We explain the transition from an ergodic region to a non trivial phase by commutativity breaking of the infinite volume limit and a suitable vanishing field. We find full agreement among theory, simulations and previous results.Comment: 23 pages, 3 figure

Transport and dynamics on open quantum graphs

We study the classical limit of quantum mechanics on graphs by introducing a Wigner function for graphs. The classical dynamics is compared to the quantum dynamics obtained from the propagator. In particular we consider extended open graphs whose classical dynamics generate a diffusion process. The transport properties of the classical system are revealed in the scattering resonances and in the time evolution of the quantum system.Comment: 42 pages, 13 figures, submitted to PR

Equilibrium statistical mechanics on correlated random graphs

Biological and social networks have recently attracted enormous attention between physicists. Among several, two main aspects may be stressed: A non trivial topology of the graph describing the mutual interactions between agents exists and/or, typically, such interactions are essentially (weighted) imitative. Despite such aspects are widely accepted and empirically confirmed, the schemes currently exploited in order to generate the expected topology are based on a-priori assumptions and in most cases still implement constant intensities for links. Here we propose a simple shift in the definition of patterns in an Hopfield model to convert frustration into dilution: By varying the bias of the pattern distribution, the network topology -which is generated by the reciprocal affinities among agents - crosses various well known regimes (fully connected, linearly diverging connectivity, extreme dilution scenario, no network), coupled with small world properties, which, in this context, are emergent and no longer imposed a-priori. The model is investigated at first focusing on these topological properties of the emergent network, then its thermodynamics is analytically solved (at a replica symmetric level) by extending the double stochastic stability technique, and presented together with its fluctuation theory for a picture of criticality. At least at equilibrium, dilution simply decreases the strength of the coupling felt by the spins, but leaves the paramagnetic/ferromagnetic flavors unchanged. The main difference with respect to previous investigations and a naive picture is that within our approach replicas do not appear: instead of (multi)-overlaps as order parameters, we introduce a class of magnetizations on all the possible sub-graphs belonging to the main one investigated: As a consequence, for these objects a closure for a self-consistent relation is achieved.Comment: 30 pages, 4 figure