  We study the dynamics of one-dimensional (1D) interacting particles simulated
with the event-chain Monte Carlo algorithm (ECMC). We argue that previous
versions of the algorithm suffer from a mismatch in the factor potential
between different particle pairs (factors) and show that in 1D models, this
mismatch is overcome by factor fields. ECMC with factor fields is motivated, in
1D, for the harmonic model, and validated for the Lennard-Jones model as well
as for hard spheres. In 1D particle systems with short-range interactions,
autocorrelation times generally scale with the second power of the system size
for reversible Monte Carlo dynamics, and with its first power for regular ECMC
and for molecular-dynamics. We show, using numerical simulations, that they
grow only with the square root of the systems size for ECMC with factor fields.
Mixing times, which bound the time to reach equilibrium from an arbitrary
initial configuration, grow with the first power of the system size.
