Discontinuous absorbing phase transitions: Minimal mechanisms and generic finite size scaling

Motivated by recent findings, we first discuss the existence of a direct and
robust mechanism providing discontinuous absorbing
transitions in short range systems with single species, with no extra symmetries or conservation laws
\footnote{Carlos E. Fiore Phys. Rev. E {\bf 89}, 022104 (2014); S. Pianegonda and C. E. Fiore, J. Stat. Mech. {\bf 2014}, P05008 (2014);
M. M. de Oliveira, M. G. E. da Luz and C. E. Fiore, (submitted).}.
We consider variants of the contact process, in
which at least two adjacent particles (instead of one, as commonly
assumed) are required to create a new species.
Many interaction rules are analyzed, including distinct cluster annihilations,
particle diffusion,
and a modified version of the original pair contact process (PCP).
Through detailed time dependent numerical simulations we find that
for our modified models, the phase transitions are of first-order,
hence contrasting with their corresponding usual formulations in the
literature, which are of second-order.
By calculating the order-parameter distributions,
the obtained bimodal shapes as well as the finite scale analysis
reinforce coexisting phases, so a discontinuous transition.
These findings strongly suggest that above particle creation requirements
constitute a minimum and fundamental mechanism
determining the phase coexistence in short-range contact processes.
Also, a phenomenological but
general finite size scaling theory is proposed for discontinuous
nonequilibrium phase transitions into absorbing states. Analogously to the equilibrium case, we show that quantities such as,
response functions, cummulants, and equal area probability distributions,
all scale with the volume, thus allowing proper estimates for the
thermodynamic limit. To illustrate these results, distinct lattice models displaying
nonequilibrium transitions -- including above examples-- are investigated. Our findings (allied to previous numerical studies in the literature)
strongly point to an unifying discontinuous phase transition scaling
behavior for equilibrium and this important class of nonequilibrium
systems.