Electron self-trapping and fluctuation density-of-states tail at the   critical point
  We consider electron self-trapping due to its interaction with order-parameter fluuctuations at the second-order phase-transition or critical point (for example, at the Curie temperature in magnetic or ferroelectric semiconductors). Using Feynman path integral approach the autolocalization energy and the size of the self-trapped state (fluctuon) are estimated. It is shown that the fluctuon states are connected with the Lifshitz tail of the electron density-of-states, the parameters of this tail being determined by the critical exponents. 
M. I. Auslender, M. I. Katsnelson