The quantitative description of cultural evolution is a challenging task. The most difficult part of the problem is probably to find the appropriate measurable quantities that can make more quantitative such evasive concepts as, for example, dynamics of cultural movements, behavioral patterns, and traditions of the people. A strategy to tackle this issue is to observe particular features of human activities, i.e., cultural traits, such as names given to newborns. We study the names of babies born in the United States from 1910 to 2012. Our analysis shows that groups of different correlated states naturally emerge in different epochs, and we are able to follow and decrypt their evolution. Although these groups of states are stable across many decades, a sudden reorganization occurs in the last part of the 20th century. We unambiguously demonstrate that cultural evolution of society can be observed and quantified by looking at cultural traits. We think that this kind of quantitative analysis can be possibly extended to other cultural traits: Although databases covering more than one century (such as the one we used) are rare, the cultural evolution on shorter timescales can be studied due to the fact that many human activities are usually recorded in the present digital era.clustering | cultural evolution | cultural traits | complex systems

We have studied the one dimensional Dyson hierarchical model in presence of a random field. This is a long range model where the interactions scale with the distance with a power law-like form J(r) ∼ r −ρ and we can explore mean field and non-mean field behavior by changing ρ. Thus, it can be used to approach the phase transitions in finite-dimensional disordered models. We studied the model at T = 0 and we numerically computed its critical exponents in the non-mean field region for Gaussian disorder. We then computed an analytic expression for the critical exponent δ, that holds in the non-mean field region, and we noted an interesting relation between the critical exponents of the disordered model and the ones of the pure model, that seems to break down in the non-mean field region. We finally compare our results for the critical exponents with the expected ones in D-dimensional short range models and with the ones of the straightforward one dimensional long range model.

The theory of glassy fluctuations can be formulated in terms of disordered effective potentials. While the properties of the average potentials are well understood, the study of the fluctuations has been so far quite limited. Close to the MCT transition, fluctuations induced by the dynamical heterogeneities in supercooled liquids can be described by a cubic field theory in presence of a random field term. In this paper, we set up the general problem of the large deviations going beyond the assumption of the vicinity to T MCT and analyze it in the paradigmatic case of spherical (p-spin) glass models. This tool can be applied to study the probability of the observation of dynamic trajectories with memory of the initial condition in regimes where, typically, the correlation C(t, 0) decays to zero at long times, at finite T and at T = 0.

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The Renormalization Group (RG) methods are still far from being completely understood in quenched disordered systems. In order to gain insight into the nature of the phase transition of these systems, it is common to investigate simple models. In this work we study a real-space RG transformation on the Dyson hierarchical lattice with a random field, which led to a reconstruction of the RG flow and to an evaluation of the critical exponents of the model at T = 0. We show that this method gives very accurate estimations of the critical exponents, by comparing our results with the ones obtained by some of us using an independent method.The Renormalization Group (RG) is a fundamental tool to study the changes of a system as observed at different scales, which has been successfully employed both in quantum field theory [1] and in the theory of second order phase transitions [2]. This process consists in integrating out small scale details of the physical systems: the original interactions between the fundamental degrees of freedom are replaced by renormalized interactions between effective degrees of freedom. Finally, the critical exponents may be computed repeating this transformation over and over [2,3]. The renormalization group has two main flavours. On the one hand, the process can be done in momentum space, by slowly integrating out high momenta [4]. Momentum space RG was first developed in quantum field theory and then it also became a highly developed tool in statistical mechanics, where it is usually performed on a perturbation expansion to compute critical exponents. On the other hand, a technically different approach is to integrate out small distance degrees of freedom in real space [2]. The advantage of the latter is to provide a more physical picture of the process despite the difficulty to obtain accurate results. In general, both methods need some approximations, but it is possible to find systems with a particular topology for which real space transformations can be performed exactly, such as the two dimensional triangular lattice [5] and the diamond hierarchical lattice [6]. These kinds of exactly soluble models could play a very important rôle to test new ideas for systems where the nature of the phase transition is difficult to understand.In this work, we focus on quenched disorder systems for which the renormalization group approach is still not deeply understood. Following the approach introduced with the diamond hierarchical lattice [7], we concentrate our effort on another hierarchical lattice which gave us the opportunity to define an approximate transformation for more realistic systems.Years ago, Dyson [8] introduced the so-called Hierarchical Model (HM) to study the problem of phase transitions in one dimensional long-range models. It was later understood that the topology of this model could be used to implement an exact real-space RG transformation [9]. Therefore, analytical and numerical studies were pursued in this direction [10], [11], [12][13][14][15]. Among the numerical works, an ...