Origin of the Growing Length Scale in M-p-Spin Glass Models

Abstract

Two versions of the M-p-spin glass model have been studied with the Migdal-Kadanoff renormalization group approximation. The model with p=3 and M=3 has at mean-field level the ideal glass transition at the Kauzmann temperature and at lower temperatures still the Gardner transition to a state like that of an Ising spin glass in a field. The model with p=3 and M=2 has only the Gardner transition. In the dimensions studied, d=2,3 and 4, both models behave almost identically, indicating that the growing correlation length as the temperature is reduced in these models -- the analogue of the point-to-set length scale -- is not due to the mechanism postulated in the random first order transition theory of glasses, but is more like that expected on the analogy of glasses to the Ising spin glass in a field.

arXiv comment5 pages, 3 figures, revised version

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• Real Space Renormalization Group Theory of Disordered Models of Glasses
• Possible instability of one-step replica symmetry breaking in p-spin Ising models outside mean-field theory
• The Super-Potts glass: a new disordered model for glass-forming liquids
• Inherent Structures in m-component Spin Glasses
• Theory of simple glasses
• Replica Symmetry Broken States of some Glass Models