Peierls transition as spatially inhomogeneous gap suppression
  We propose a model of the Peierls transition (PT) taking into account amplitude fluctuations of the charge-density waves and spontaneous thermally activated suppression of the Peierls gap, akin to the phase slip process. The activation results in the exponential growth of the normal phase with increasing temperature. The model fairly describes the behavior of resistance, thermal expansion, Young modulus and specific heat both below and above the PT temperature $T_P$. The PT appears to have a unique nature: it does not comprise $T_P$ as a parameter, and at the same time it has features of the 1st order transition. The possible basis for the model is activation of non-interacting amplitude solitons perturbing large volumes around them. 
V.Ya. Pokrovskii, A.V. Golovnya, and S.V. Zaitsev-Zotov