| 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 $\le n+1$ . 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 $\rho \le \rho_c = \frac{1}{n+1}$ , to an active state for $\rho > \rho_c$ . The mean fraction of movable particles in the active steady state varies as $(\rho - \rho_c)^{\beta}$ , for ρ near $\rho_c$ . We show that for the model with range n, the exponent $\beta =n$ , and thus can be made arbitrarily large.
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