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We consider electron self-trapping due to its interaction withorder-parameter fluuctuations at the second-order phase-transition or criticalpoint (for example, at the Curie temperature in magnetic or ferroelectricsemiconductors). Using Feynman path integral approach the autolocalizationenergy and the size of the self-trapped state (fluctuon) are estimated. It isshown that the fluctuon states are connected with the Lifshitz tail of theelectron density-of-states, the parameters of this tail being determined by thecritical exponents.Comment: 4 pages, revtex4, Phys. Rev. B, accepte

Electron self-trapping and the fluctuation density-of-states tail at the critical point