How many is different? Ideal bose gas revisited Seminar

How many H2O molecules are needed to form water? While the precise answer is not known, it is clear that the answer should be a finite number. We carefully revisit the ideal Bose gas confined in a cubic box which is discussed in most statistical physics textbooks. We report that the isobar of the ideal gas zigzags on the temperature-volume plane provided the number of particles is 'finitely' large enough. This may demonstrate for the first time how finite systems can feature mathematical singularities, realizing the notion of 'Emergence'.