New Results for the Correlation Functions of the Ising Model and the Transverse Ising Chain

In this paper we show how an infinite system of coupled Toda-type nonlinear differential equations derived by one of us can be used efficiently to calculate the time-dependent pair-correlations in the Ising chain in a transverse field. The results are seen to match extremely well long large-time asymptotic expansions newly derived here. For our initial conditions we use new long asymptotic expansions for the equal-time pair correlation functions of the transverse Ising chain, extending an old result of T.T. Wu for the 2d Ising model. Using this one can also study the equal-time wavevector-dependent correlation function of the quantum chain, a.k.a. the q-dependent diagonal susceptibility in the 2d Ising model, in great detail with very little computational effort.Comment: LaTeX 2e, 31 pages, 8 figures (16 eps files). vs2: Two references added and minor changes of style. vs3: Corrections made and reference adde

Desenvolvimento de Adiantopsis radiata, Pteris denticulata (Pteridaceae) e Polypodium latipes (Polypodiaceae) em condições naturais Development of Adiantopsis radiata, Pteris denticulata (Pteridaceae) e Polypodium latipes (Polypodiaceae) in natural conditions

Populações de gametófitos e esporófitos àe Adiantopsis radiata (L.) Fée, Pteris denticulata Sw. e Polypodium latipes Langsd. et Fisch, ocorrentes em mata mesofítica semidecídua do Estado de São Paulo, Brasil, foram acompanhadas em campo durante 24 meses e amostras coletadas para estudo em laboratório. A morfologia das diferentes fases de desenvolvimento, desde o gametófito até o esporófito adulto, bem como informações relativas ao comportamento das espécies em função de condições de dessecamento são apresentadas.<br>Populations of gametophytes and sporophytes of Adiantopsis radiata (L.) Fée, Pteris denticulata Sw. and Polypodium latipes Langsd. et Fisch, occurring in a semideciduous mesophytic forest in the State of São Paulo, Brazil, were observed during 24 months and samples were collected for study in the laboratory. The morphology of different phases of development, from gametophytes until the formation of adult sporophytes, as well as informations relative to their behavior in conditions of reduced humidity are presented