Universal Critical Behavior of Aperiodic Ferromagnetic Models

We investigate the effects of geometric fluctuations, associated with aperiodic exchange interactions, on the critical behavior of $q$-state ferromagnetic Potts models on generalized diamond hierarchical lattices. For layered exchange interactions according to some two-letter substitutional sequences, and irrelevant geometric fluctuations, the exact recursion relations in parameter space display a non-trivial diagonal fixed point that governs the universal critical behavior. For relevant fluctuations, this fixed point becomes fully unstable, and we show the apperance of a two-cycle which is associated with a novel critical behavior. We use scaling arguments to calculate the critical exponent $\alpha$ of the specific heat, which turns out to be different from the value for the uniform case. We check the scaling predictions by a direct numerical analysis of the singularity of the thermodynamic free-energy. The agreement between scaling and direct calculations is excellent for stronger singularities (large values of $q$). The critical exponents do not depend on the strengths of the exchange interactions.Comment: 4 pages, 1 figure (included), RevTeX, submitted to Phys. Rev. E as a Rapid Communicatio

Growth of pea plants (Pisum sativum L.) subjected to different soil water potentials : physiological indexes

A ervilha é cultivada no Brasil Central, durante o inverno seco, exigindo para o pleno êxito da cultura o uso da irrigação. Assim, o presente trabalho se propõe a avaliar os efeitos do potencial da água no solo nos índices fisiológicos da análise quantitativa de crescimento de plantas de ervilha (Pisum sativum L.). O experimento foi montado em casa de vegetação, em solos de textura argilosa, com delineamento experimental inteiramente casualizado, com quatro tratamentos decorrentes de potenciais mínimos da água no solo (-33, -100, -200 e -1500 kPa) em três repetições, cada qual contendo duas plantas de ervilha, cultivar Caprice. Os resultados obtidos evidenciaram que a redução do potencial água no solo, induziu o decréscimo na área foliar, sem interferir no comportamento da razão de massa foliar, razão de área foliar, taxa assimilatória líquida e taxa de crescimento relativo. _________________________________________________________________________________________ ABSTRACT: Peas are cultivated in the central region of Brazil, during the dry winter, demanding for the complete success the use of irrigation. Therefore, the present work has the aim of evaluating soil water potential effects on the indexes of physiological growth analysis of peas (Pisum sativum L.). The experiment was carried out in a greenhouse using soils of clayey texture, in a fully randomized design, with four treatments, based on minimum soil water potentials (-33, -100, -200 and -1500 kPa) in three replicates, each one containing two pea plants Caprice cultivar. The results obtained indicate that the reduction of soil water potential induced the decrease of leaf area, but did not interfer on the behaviour of leaf weight ratio, leaf area ratio, net assimilation rate and relative growth rate