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Predictive power of MCT: numerical testing and finite size scaling for a mean field spin glass

T. Sarlat,A. Billoire,G. Biroli,J. Bouchaud

Published 2009 in Journal of Statistical Mechanics: Theory and Experiment

ABSTRACT

The aim of this paper is to test numerically the predictions from the mode-coupling theory (MCT) of the glass transition and study its finite size scaling properties in a model with an exact MCT transition, which we choose to be the fully connected random orthogonal model. Surprisingly, some predictions are verified while others seem clearly violated, with inconsistent values of some MCT exponents. We show that this is due to strong pre-asymptotic effects that disappear only in a surprisingly narrow region around the critical point. Our study of finite size scaling (FSS) shows that standard theory valid for pure systems fails because of strong sample to sample fluctuations. We propose a modified form of FSS that accounts well for our results. En passant, we also give new theoretical insights into FSS in disordered systems above their upper critical dimension. Our conclusion is that the quantitative predictions of MCT are exceedingly difficult to test even for models for which MCT is exact. Our results highlight that some predictions are more robust than others. This could provide useful guidance when dealing with experimental data.

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