A simple model of non-self-averaging effects and its relevance to reproducibility of experiments

In condensed matter physics we tend to take it for granted that if we prepare two macroscopic samples in identical fashion they will have the same thermodynamic properties in equilibrium. In the case of disordered systems, such as glasses, this is sometimes termed reproducibility; the assumption that we can reproduce an experimental result if we prepare a sample in an identical fashion as in our previous experiment.

It is possible to show that there are models of disordered systems where certain properties are not reproducible and that this is a consequence of a lack of self-averaging in the underlying random variables. In this theory club talk I will work through a very simple model of sums of random numbers which show non-self-averaging properties and indicate how this relates to subtle failures in reproducibility. The underlying mechanism in this simple system is identical to that of much more realistic models.