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In this paper we study finite interaction range corrections to the mosaicpicture of the glass transition as emerges from the study of the Kac limit oflarge interaction range for disordered models. To this aim we consider point toset correlation functions, or overlaps, in a one dimensional random energymodel as a function of the range of interaction. In the Kac limit, the mosaiclength defines a sharp first order transition separating a high overlap phasefrom a low overlap one. Correspondingly we find that overlap curves as afunction of the window size and different finite interaction ranges crossroughly at the mosaic lenght. Nonetheless we find very slow convergence to theKac limit and we discuss why this could be a problem for measuring the mosaiclenght in realistic models.

Mosaic length and finite interaction-range effects in a one dimensional random energy model