Study of the atom-phonon coupling model for (SC) partition function: first order phase transition for an infinite linear chainJamil A. Nasser, Luc Chassagne, Suat Topçu, Jorge Linares and Yasser AlayliEur. Phys. J. B, 87 3 (2014) 69DOI: https://doi.org/10.1140/epjb/e2014-41039-0