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

摘要

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 ≤ n + 1. 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 ρ ≤ ρ_c = 1n+1, to an active state for ρ > ρc. The mean fraction of movable particles in the active steady state varies as (ρ - ρc)~β, for ρ near ρc. We show that for the model with range n, the exponent β = n, and thus can be made arbitrarily large.