title: Dynamics and termination cost of spatially coupled mean-field models.
abstract: This work is motivated by recent progress in information theory and signal processing where the so-called spatially coupled design of systems leads to considerably better performance. We address relevant open questions about spatially coupled systems through the study of a simple Ising model. In particular, we consider a chain of Curie-Weiss models that are coupled by interactions up to a certain range. Indeed, it is well known that the pure (uncoupled) Curie-Weiss model undergoes a first-order phase transition driven by the magnetic field, and furthermore in the spinodal region such systems are unable to reach equilibrium in subexponential time if initialized in the metastable state. In contrast, the spatially coupled system is instead able to reach the equilibrium even when initialized to the metastable state. The equilibrium phase propagates along the chain in the form of a traveling wave. Here we study the speed of the wave front and the so-called termination cost-i.e., the conditions necessary for the propagation to occur. We reach several interesting conclusions about optimization of the speed and the cost.
authors.affiliation: Institut de Physique Théorique, CEA, CNRS-URA 2306, F-91191, Gif-sur-Yvette, France.
authors.forename: Francesco
authors.initials: F
authors.lastname: Caltagirone
authors.affiliation: Laboratoire de Physique Théorique et Modèles Statistiques, Université Paris-Sud 11 and CNRS UMR8626, Batiment 100, 91405 Orsay, France.
authors.forename: Silvio
authors.initials: S
authors.lastname: Franz
authors.affiliation: Institut de Physique Théorique, CEA, CNRS-URA 2306, F-91191, Gif-sur-Yvette, France.
authors.forename: Richard G
authors.initials: RG
authors.lastname: Morris
authors.affiliation: Institut de Physique Théorique, CEA, CNRS-URA 2306, F-91191, Gif-sur-Yvette, France.
authors.forename: Lenka
authors.initials: L
authors.lastname: Zdeborová