Topological and Dynamic Phase Transitions in Statistical Physics
Recently we have developed a dynamic transition theory, leading to a general principle that all dynamic transitions for dissipative systems can be classified into three categories: continuous, catastrophic and random. We use the dynamic transition theory to study equilibrium phase transition in statistical physics. First we show that there exist only first, second and third order transitions. Second, we demonstrate that the discrepancy for critical exponents between theory and the experiment is due to fluctuations.
The second part of the talk is on topological phase transitions. Historically, J. Michael Kosterlitz and David J. Thouless (1972, 1973) identified a completely new type of phase transition in 2D systems where topological defects play a crucial role. With this work, they received 2016 Nobel prize in physics. Intuitively speaking, topological phase transition studies the change of the topological structure in the physical space as certain system parameter crosses a critical threshold. In this part of the talk, we focus on two typical examples of topological phase transitions: quantum phase transition and boundary-layer separation of incompressible fluid flows. This is joint work with Tian Ma.