Emergent phenomena in physics

In the historical development of physics, the idea of reduction has been a fundamental guiding pricinple which has played a most important role in many celebrated achievements of the past decades. However, when cooperative phenomena in complex systems are investigated on the basis of reduction, the theories have encountered enormous difficulties and challenges. Thus, emergent principles have to be established, and these have become a new paradigm in current theoretical research. This article will present a comprehensive discussion about the developments of prototype emergent phenomena in condensed matter physics, addressing various important topics, useful treatments, and major advances.