DOI: 10.1051/jp1:1993227
J. Phys. I France 3 (1993) 1993-2006

Lack of self-averaging in weakly disordered one-dimensional systems

A. Crisanti¹, G. Paladin², M. Serva³ and A. Vulpiani<sup>1

1</sup>  Dipartimento di Fisica, Università "La Sapienza" p.le Moro 5, 1-00185, Roma, Italy
²  Dipartimento di Fisica, Università dell'Aquila, 1-67100 Coppito, L'Aquila, Italy
³  Dipartimento di Matematica, Università dell'Aquila, 1-67100 Coppito, L'Aquila, Italy

(Received 15 April 1993, accepted 1 July 1993)

Abstract
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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