We study the Bose-Einstein condensation phase transition in a weakly interacting gas through a perturbative analysis of finite systems. In both the grand canonical and the canonical ensembles, perturbation theory suffers from infrared divergences and cannot directly determine the transition temperature in the thermodynamic limit. However, in conjunction with finite size scaling, perturbation th...

Symmetry breaking plays a pivotal role in modern physics. Although self-similarity is also symmetry and appears ubiquitously nature, fundamental question whether makes sense or not. Here, by identifying the most important kind of critical fluctuations dubbed as phases comparing consequences having with those lacking fluctuations, we show that can indeed be broken significant at least nonequilib...