The distribution N(x) of citations of scientific papers has recently been illustrated (on ISI and PRE data sets) and analyzed by Redner [Eur. Phys. J. B 4, 131 (1998)]. To fit the data, a stretched exponential (N(x) ∝ exp −(x/x 0 ) β ) has been used with only partial success. The success is not complete because the data exhibit, for large citation count x, a power law (roughly N(x) ∝ x −3 for the ISI data), which, clearly, the stretched exponential does not reproduce. This fact is then attributed to a possibly different nature of rarely cited and largely cited papers. We show here that, within a nonextensive thermostatistical formalism, the same data can be quite satisfactorily fitted with a single curve (namely, N(x) ∝ 1/[1 + (q − 1) λ x] q q−1 for the available values of x. This is consistent with the connection recently established by Denisov [Phys. Lett. A 235, 447 (1997)] between this nonextensive formalism and the Zipf-Mandelbrot law. What the present analysis ultimately suggests is that, in contrast to Redner's conclusion, the phenomenon might essentially be one and the same along the entire range of the citation number x.

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We have studied the role of long-range interactions on the thermodynamics of magnetic systems. We have simulated, through the Monte Carlo method, magnetization curves of a two-dimensional classical Ising model including a long-range dipole-dipole-like interaction, where the range of interaction is tuned by a parameter ␣. Based on the conjectures of Tsallis statistics, we show that, for ␣/dр1 (dϭ2), the appropriate form of the equation of state is given by M /Nϭm(T*,H*) with T*ϵT/N* and H*ϵH/N*. The normalization factor N*͓N*ϵ(N (1Ϫ␣/d) Ϫ1)/(1Ϫ␣/d)͔ emerges from the nonextensivity of thermodynamic variables of energy type. The crossover from nonextensive to extensive behavior at ␣/dϭ1 occurs smoothly and similarly to other quite different systems, thus suggesting it to be a general result. ͓S0163-1829͑97͒06009-8͔ PHYSICAL REVIEW B

In this work we have studied the research activity for countries of Europe, Latin America and Africa for all sciences between 1945 and November 2008. All the data are captured from the Web of Science database during this period. The analysis of the experimental data shows that, within a nonextensive thermostatistical formalism, the Tsallis q-exponential distribution N(c) satisfactorily describes Institute of Scientific Information citations. The data which are examined in the present survey can be fitted successfully as a first approach by applying a single curve (namely, NðcÞ / 1=½1 þ ðq À 1Þ c=T 1 qÀ1 with q4 /3 for all the available citations c, T being an ''effective temperature''. The present analysis ultimately suggests that the phenomenon might essentially be one and the same along the entire range of the citation number. Finally, this manuscript provides a new ranking index, via the ''effective temperature'' T, for the impact level of the research activity in these countries, taking into account the number of the publications and their citations.