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Phase transition in the Peierls model for polyacetylene

Gontier, David; Kouande, Adéchola; Séré, Eric (2023), Phase transition in the Peierls model for polyacetylene, Annales Henri Poincaré. 10.1007/s00023-023-01299-w

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Article accepté pour publication ou publié
Date
2023
Journal name
Annales Henri Poincaré
Publisher
Springer
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Author(s)
Gontier, David
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Kouande, Adéchola
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Séré, Eric
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
We consider the Peierls model for closed polyactetylene chains with an even number of carbon atoms as well as infinite chains, in the presence of temperature. We prove the existence of a critical temperature below which the chain is dimerized, and above which it is 1-periodic. The chain behaves like an insulator below the critical temperature and like a metal above it. We characterize the critical temperature in the thermodynamic limit model, and prove that it is exponentially small in the rigidity of the chain. We study the phase transition around this critical temperature.