Eur. Phys. J. B 27, 363-380 (2002)
https://doi.org/10.1140/epjb/e2002-00167-0

Jamming, freezing and metastability in one-dimensional spin systems

¹ Service de Physique Théorique (URA 2306 of CNRS) , CEA Saclay, 91191 Gif-sur-Yvette Cedex, France
² Service de Physique de l'État Condensé, CEA Saclay, 91191 Gif-sur-Yvette Cedex, France

Corresponding author: ^a luck@spht.saclay.cea.fr

Received: 26 February 2002
Published online: 6 June 2002

Abstract

We consider in parallel three one-dimensional spin models with kinetic constraints: the paramagnetic constrained Ising chain, the ferromagnetic Ising chain with constrained Glauber dynamics, and the same chain with constrained Kawasaki dynamics. At zero temperature the dynamics of these models is fully irreversible, leading to an exponentially large number of blocked states. Using a mapping of these spin systems onto sequential adsorption models of, respectively, monomers, dimers, and hollow trimers, we present exact results on the statistics of blocked states. We determine the distribution of their energy or magnetization, and in particular the large-deviation function describing its exponentially small tails. The spin and energy correlation functions are also determined. The comparison with an approach based on a priori statistics reveals systematic discrepancies with the Edwards hypothesis, concerning in particular the fall-off of correlations.