Modulated phases and devil's staircases in a layered mean-field version of the ANNNI model

We investigate the phase diagram of a spin-$1/2$ Ising model on a cubic lattice, with competing interactions between nearest and next-nearest neighbors along an axial direction, and fully connected spins on the sites of each perpendicular layer. The problem is formulated in terms of a set of noninteracting Ising chains in a position-dependent field. At low temperatures, as in the standard mean-feild version of the Axial-Next-Nearest-Neighbor Ising (ANNNI) model, there are many distinct spatially commensurate phases that spring from a multiphase point of infinitely degenerate ground states. As temperature increases, we confirm the existence of a branching mechanism associated with the onset of higher-order commensurate phases. We check that the ferromagnetic phase undergoes a first-order transition to the modulated phases. Depending on a parameter of competition, the wave number of the striped patterns locks in rational values, giving rise to a devil's staircase. We numerically calculate the Hausdorff dimension $D_{0}$ associated with these fractal structures, and show that $D_{0}$ increases with temperature but seems to reach a limiting value smaller than $D_{0}=1$.Comment: 17 pages, 6 figure

Introdução de clones de guaraná no cerrado do Amapá.

As pesquisas com guaraná (Paullinia cupana var. sorbilis) no norte do Brasil são feitas geralmente em áreas de mata de terra firme. Seu comportamento nos cerrados, que abrangem cerca de 12.973 km2 no Amapá, e pouco conhecido.bitstream/item/65102/1/AP-1988-introducao-clones-guarana-cerrado-amapa.pd

Plantas forrageiras identificadas na região de Ouricuri-PE.

Com o objetivo de informar sobre as principais forrageiras da região de Ouricuri-PE, compreendendo partes dos municípios de Bodoco, Ipubi, Trindade. Ouricuri e Parnamirim, foi feita uma triagem das espécies detectadas em questionários aplicados nos trabalhos de levantamento Fitoecologicos, alem de prospecções de campo