A class of exactly solved assisted hopping models of active-absorbing state transitions on a line

Abstract

We construct a class of assisted hopping models in one dimension in which a particle can move only if it does not lie in an otherwise empty interval of length greater than $n+1$. 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 $\rho$ 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 $\rho$ near ${\rho }_c$. We show that for the model with range $n$, the exponent $\beta =n$, and thus can be made arbitrarily large.

4 pages

References in corpus (5)

• Fixed-Energy Sandpiles Belong Generically to Directed Percolation
• Active Absorbing State Phase Transition Beyond Directed Percolation : A Class of Exactly Solvable Models
• Facilitated Asymmetric Exclusion
• Activated Random Walkers: Facts, Conjectures and Challenges
• The phase transition of the diffusive pair contact process revisited

Cited by in corpus (4)

• Dynamic correlations in the conserved Manna sandpile
• Exclusion Processes with Avalanches
• Multi-critical absorbing phase transition in a class of exactly solvable models
• Multi-chain models of Conserved Lattice Gas