  The environment within dark matter haloes can quench the star formation of
galaxies. However, environmental effects beyond the virial radius of haloes
($\gtrsim$ 1 Mpc) are less evident. An example is the debated correlation
between colour or star formation in central galaxies and neighbour galaxies in
adjacent haloes at large separations of several Mpc, referred to as two-halo
galactic conformity. We use two galaxy catalogues generated from different
versions of the semi-analytic model SAG applied to the MDPL2 cosmological
simulation and the IllustrisTNG300 cosmological hydrodynamical simulation to
study the two-halo conformity by measuring the quenched fraction of
neighbouring galaxies as a function of the real-space distance from central
galaxies. We find that low-mass central galaxies in the vicinity of massive
systems ($M_{\rm 200c}$ $\geq$ 10$^{13}$ $h^{-1}~\rm M_{\odot}$) out to 5
$h^{-1}$ Mpc are preferentially quenched compared to other central galaxies at
fixed stellar mass $M_{\star}$ or fixed host halo mass $M_{\rm 200c}$ at $z$ ~
0. In all the galaxies catalogues is consistent that the low-mass ($M_{\star} <
10^{10}$ $h^{-1}~\rm M_{\odot}$ or $M_{\rm 200c} < 10^{11.8}$ $h^{-1}~\rm
M_{\odot}$) central galaxies in the vicinity of clusters and, especially,
groups of galaxies mostly produce the two-halo galactic conformity. On average,
the quenched low-mass central galaxies are much closer to massive haloes than
star-forming central galaxies of the same mass (by a factor of ~5). Our results
agree with other works regarding the environmental influence of massive haloes
that can extend beyond the virial radius and affect nearby low-mass central
galaxies.
