Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2007-11-29
J. Phys. A: Math. Theor. 41 (2008) 324011
Physics
Condensed Matter
Disordered Systems and Neural Networks
18 pages, 7 figures, contribution for the special issue "Viewing the World through Spin Glasses" in honour of Professor David
Scientific paper
10.1088/1751-8113/41/32/324011
In this paper we study finite interaction range corrections to the mosaic picture of the glass transition as emerges from the study of the Kac limit of large interaction range for disordered models. To this aim we consider point to set correlation functions, or overlaps, in a one dimensional random energy model as a function of the range of interaction. In the Kac limit, the mosaic length defines a sharp first order transition separating a high overlap phase from a low overlap one. Correspondingly we find that overlap curves as a function of the window size and different finite interaction ranges cross roughly at the mosaic lenght. Nonetheless we find very slow convergence to the Kac limit and we discuss why this could be a problem for measuring the mosaic lenght in realistic models.
Franz Silvio
Parisi Giorgio
Ricci-Tersenghi Federico
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