Phase transition in the 3-D massive Gross-Neveu model

We consider the 3-dimensional massive Gross-Neveu model at finite temperature as an effective theory for strong interactions. Using the Matsubara imaginary time formalism, we derive a closed form for the renormalized $T$-dependent four-point function. This gives a singularity, suggesting a phase transition. Considering the free energy we obtain the $T$-dependent mass, which goes to zero for some temperature. These results lead us to the conclusion that there is a second-order phase transition.Comment: 06 pages, 02 figures, LATE

Phase transition in the massive Gross-Neveu model in toroidal topologies

We use methods of quantum field theory in toroidal topologies to study the $N$-component $D$-dimensional massive Gross-Neveu model, at zero and finite temperature, with compactified spatial coordinates. We discuss the behavior of the large-$N$ coupling constant ($g$), investigating its dependence on the compactification length ($L$) and the temperature ($T$). For all values of the fixed coupling constant ($\lambda$), we find an asymptotic-freedom type of behavior, with $g\to 0$ as $L\to 0$ and/or $T\to \infty$. At T=0, and for $\lambda \geq \lambda_{c}^{(D)}$ (the strong coupling regime), we show that, starting in the region of asymptotic freedom and increasing $L$, a divergence of $g$ appears at a finite value of $L$, signaling the existence of a phase transition with the system getting spatially confined. Such a spatial confinement is destroyed by raising the temperature. The confining length, $L_{c}^{(D)}$, and the deconfining temperature, $T_{d}^{(D)}$, are determined as functions of $\lambda$ and the mass ($m$) of the fermions, in the case of $D=2,3,4$. Taking $m$ as the constituent quark mass ($\approx 350\: MeV$), the results obtained are of the same order of magnitude as the diameter ($\approx 1.7 fm$) and the estimated deconfining temperature ($\approx 200\: MeV$) of hadrons.Comment: 14 pages, 10 figures, 1 table, to appear in Phys. Rev.

Crescimento inicial de milho em solo adubado com diferentes compostos orgânicos.

Foram elaborados cinco compostos orgânicos com diferentes composições, todos a base de esterco caprino, bagaço de coco e capim elefante, enriquecidos com torta de mamona, fosfato natural de gafsa e sulfato de potássio, de modo que, a final, cada pilha tivesse concentrações diferenciadas de nutrientes. O experimento foi montado em vasos contendo solo e os compostos preparados, dispostos em delineamento experimental inteiramente casualisado,, com seis tratamentos, sendo uma testemunha, e quatro repetições. Aos 28 dias após o plantio foi efetuado o corte das plantas, avaliando-se o número de folhas, a altura das plantas, o diâmetro do colo e o peso de matéria seca. De um modo geral, os compostos promoveram maior crescimento das plantas de milho que a testemunha (sem composto) com destaque para o composto de número 22 (77% de bagaço de coco, 20% de esterco caprino e 3% de sulfato de potássio)

Tratamento da mastite subclínica de ovelhas no período seco com antimicrobiano convencional e antimicrobiano nanoparticulado.

Dissertação sob orientação do Pesquisador Luiz Francisco Zafalo

Cultivo de mangueira Tommy Atkins com diferentes compostos orgânicos.

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