Persistence of order on ferromagnetic models in the presence of quasi random auto-similar fields / Persistência de ordem em modelos ferromagnéticos na presença de campos auto-similares quase aleatórios"

AUTOR(ES)
DATA DE PUBLICAÇÃO

2007

RESUMO

In this work we study the existence of long range order for ferromagnetic models in the presence of an external field whose configuration has a pattern typically random. We prove, via the Peierlsargument modified by Griffiths in his study of an antiferromagnet, that the two dimensional ferromagnetic Ising model for a staggered field exhibits long-range order at finite temperature and small field intensity. We propose to give a further step considering sparse self similar fields, whose sum is zero in all scales. We study as well the hierarchical model in two dimensions, where we prove existence of long-range order at finite temperature in the absence of external field and for a field configuration with sparse irregular regions. We prove that the results for the two-dimensional hierarchical contours model are equivalent to the results of the hierarchical model in two dimensions. Lastly, we prove via infrared bound method, existence of long range order in the N-vector model with a staggered and weak external field for d >= 3, under the hypothesis that the variance of the state connected with the field interaction has cardinality lower than volume. We show, under similar hypotheses, that the N-vector hierarchical model with a sparse field of low intensity has long range ordem at low temperatures.

ASSUNTO(S)

argumento de peierls hierarchical contours model modelo n-vetorial long range order n-vector model peierls argument hierarchical n-vector model modelo de contornos hierárquicos dyson hierarchical model ising model ordem de logo alcance modelo ising modelo hierarquico de dyson modelo n-vetorial hierárquico

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