One of the key concepts in physics is that of a phase transition. Ice melting to form water is one example; another is the transition between magnetic and non-magnetic forms of iron. The underlying physics of these transitions is a story about correlations. Understanding a phase transition and, indeed, a phase of matter, is all about understanding the growth of correlations.
You would think that one of the cleanest and best understood physical systems wouldn't have a lot to offer physicists in terms of understanding correlations that develop through a phase transition. However, physicists got a bit of a surprise when they looked at particular correlations that arise as a dilute gas is cooled down until it forms a Bose Einstein condensate (BEC).