A class of exactly solved assisted-hopping models of active-inactive state transition on a line

Department of Theoretical Physics, Tata Institute of Fundamental Research - Homi Bhabha Road, Mumbai 400005, India

Received: 7 August 2013
Accepted: 19 October 2013

Abstract

We construct a class of assisted-hopping models in one dimension in which a particle can move only if it has exactly one occupied neighbour, or if it lies in an otherwise empty interval of length . We determine the exact steady state by a mapping to a gas of defects with only on-site interaction. We show that this system undergoes a phase transition as a function of the density ρ of particles, from a low-density phase with all particles immobile for , to an active state for . The mean fraction of movable particles in the active steady state varies as , for ρ near . We show that for the model with range n, the exponent , and thus can be made arbitrarily large.