Lack of self-average in weakly disordered one dimensional systems

Details Lack of self-average in weakly disordered one dimensional systems Lack of self-average in weakly disordered one dimensional systems

1993-04-16

arxiv.org/abs/cond-mat/9304025v1

Physics

Condensed Matter

17 pages + 5 figures, TeX dialect: Plain TeX + IOP macros (included)

Scientific paper

10.1051/jp1:1993227

We introduce a one dimensional disordered Ising model which at zero temperature is characterized by a non-trivial, non-self-averaging, overlap probability distribution when the impurity concentration vanishes in the thermodynamic limit. The form of the distribution can be calculated analytically for any realization of disorder. For non-zero impurity concentration the distribution becomes a self-averaging delta function centered on a value which can be estimated by the product of appropriate transfer matrices.

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