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

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 withan exact MCT transition, which we choose to be the fully connected randomorthogonal model. Surprisingly, some predictions are verified while others seem clearlyviolated, with inconsistent values of some MCT exponents. We show that this is dueto strong pre-asymptotic effects that disappear only in a surprisingly narrowregion around the critical point. Our study of finite size scaling (FSS) shows thatstandard theory valid for pure systems fails because of strong sample to samplefluctuations. We propose a modified form of FSS that accounts well for our results. Enpassant, we also give new theoretical insights into FSS in disordered systemsabove their upper critical dimension. Our conclusion is that the quantitativepredictions of MCT are exceedingly difficult to test even for models for whichMCT is exact. Our results highlight that some predictions are more robust thanothers. This could provide useful guidance when dealing with experimental data.