Lyapunov exponents as a dynamical indicator of a phase transition

PACS. 05.45.-a – Nonlinear dynamics and nonlinear dynamical systems. PACS. 05.70.Fh – Phase transitions: general studies. PACS. 02.40.-k – Geometry, differential geometry, and topology. Abstract. – We study analytically the behavior of the largest Lyapunov exponent λ1 for a one-dimensional chain of coupled nonlinear oscillators, by combining the transfer integral method and a Riemannian geometry approach. We apply the results to a simple model, proposed for the DNA denaturation, which emphasizes a first-order–like or second-order phase transition depending on the ratio of two length scales: this is an excellent model to characterize λ1 as a dynamical indicator close to a phase transition. Introduction. – Phase transition plays a central role in equilibrium and nonequilibrium statistical physics books and lectures in particular because it exemplifies the paradigmatic concept of universality in physics. In the theory of dynamical systems, the concept of Lyapunov exponent has also attracted a lot of attention [1,2] because it defines unambiguously a sufficient condition for chaotic instability, but unfortunately except for very few systems it is alread