 One of the most striking macroscopic feature of systems is the existence of multiple phases (gas, liquid and solid, for example, or diamagnetic and ferromagnetic for another) and the transitions between those phases as thermodynamic features such as temperature and pressure or imposed magnetization are varied.  Early work on phase transitions focused on the way in which quantities changed in a non-analytic manner from phase to phase, even though statistical mechanics seemed to show that such non-analytic behavior was impossible, at least for systems with a finite number of constituents. Here resort was often to going to the “thermodynamic limit” of an idealized infinite system.