Zipf's law is shown to arise as the variational solution of a problem formulated in Fisher's terms. An appropriate minimization process involving Fisher information and scale-invariance yields this universal rank distribution. As an example we show that the number of citations found in the most referenced physics journals follows this law.

The minimization of Fisher's information (MFI) approach of Frieden et al. [Phys. Rev. E 60 48 (1999)] is applied to the study of size distributions in social groups on the basis of a recently established analogy between scale invariant systems and classical gases [arXiv:0908.0504]. Going beyond the ideal gas scenario is seen to be tantamount to simulating the interactions taking place in a network's competitive cluster growth process. We find a scaling rule that allows to classify the final cluster-size distributions using only one parameter that we call the competitiveness. Empirical city-size distributions and electoral results can be thus reproduced and classified according to this competitiveness, which also allows to correctly predict well-established assessments such as the "six-degrees of separation", which is shown here to be a direct consequence of the maximum number of stable social relationships that one person can maintain, known as Dunbar's number. Finally, we show that scaled city-size distributions of large countries follow the same universal distribution. PACS. 89.70.Cf Entropy and other measures of information -05.90.+m Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems -89.75.Da Systems obeying scaling laws -89.75.-k Complex systems

For the first time, the morphology and dynamics of spin avalanches in Mn12-Acetate crystals using magneto-optical imaging has been explored. We observe an inhomogeneous relaxation of the magnetization, the spins reversing first at one edge of the crystal and a few milliseconds later at the other end. Our data fit well with the theory of magnetic deflagration, demonstrating that very slow deflagration rates can be obtained, which makes new types of experiments possible.

The different magnetic phases of the intermetallic compound Nd 5 Ge 3 are studied in terms of the specific heat, in a broad range of temperatures (350 mK-140 K) and magnetic fields (up to 40 kOe).The expected T 3 and T 3/2 terms are not found in the antiferromagnetic (AFM) and ferromagnetic (FM) phases respectively, but a gapped T 2 contribution that originates from a mixture of AFM and FM interactions in different dimensionalities under a large magnetocrystalline anisotropy, is present in both. An almost identical Schottky anomaly, that arises from the hyperfine splitting of the nuclear levels of the Nd 3+ ions, is observed in both phases, which leads us to state that the magnetic-field induced transition AFM→FM that the system experiments below 26 K consists in the flip of the magnetic moments of the Nd ions, conserving the average local moment.

We report magnetic deflagration phenomena ocurring in both antiferromagnetic and ferromagnetic phases in a single crystal of the intermetallic compound Nd 5 Ge 3 . We have investigated, using a trigger heat pulse, the spatial and time-resolved evolution of induced magnetic avalanches as a function of the applied magnetic field. The experimental data fit well with the theory of magnetic deflagration.