## Abstract

We obtain the exact solution of the facilitated totally asymmetric simple exclusion process (F-TASEP) in 1D. The model is closely related to the conserved lattice gas (CLG) model and to some cellular automaton traffic models. In the F-TASEP a particle at site j in Z jumps, at integer times, to site j + 1, provided site j - 1 is occupied and site j + 1 is empty. When started with a Bernoulli product measure at density ρ, the system approaches a stationary state. This non-equilibrium steady state (NESS) has phase transitions at ρ = 1/2 and ρ = 2/3. The different density regimes 0 <ρ < 1/2, 1/2 <ρ < 2/3, and 2/3 <ρ < 1 exhibit many surprising properties; for example, the pair correlation g(j) = <η(i) η (i + j)> satisfies, for all n ∈ Z, Σ^{k(n+1)} _{j=kn+1} g(j) = kρ^{2}, with k = 2 when 0 ≤ ρ ≤ 1/2, k = 6 when 1/2 ≤ ρ ≤ 2/3, and k = 3 when 2/3 ≤ ρ ≤ 1. The quantity lim_{L→∞} V_{L}/L, where V_{L} is the variance in the number of particles in an interval of length L, jumps discontinuously from ρ (1 - ρ) to 0 when ρ → 1/2 and when ρ → 2/3.

Original language | English (US) |
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Article number | 123202 |

Journal | Journal of Statistical Mechanics: Theory and Experiment |

Volume | 2019 |

Issue number | 12 |

DOIs | |

State | Published - Dec 4 2019 |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Statistics and Probability
- Statistics, Probability and Uncertainty

## Keywords

- absorbing states
- exact results
- exclusion processes