  Differential cross-section measurements are presented for the electroweak
production of two jets in association with a $Z$ boson. These measurements are
sensitive to the vector-boson fusion production mechanism and provide a
fundamental test of the gauge structure of the Standard Model. The analysis is
performed using proton-proton collision data collected by ATLAS at
$\sqrt{s}$=13 TeV and with an integrated luminosity of 139 fb$^{-1}$. The
differential cross-sections are measured in the $Z\rightarrow \ell^+\ell^-$
decay channel ($\ell=e,\mu$) as a function of four observables: the dijet
invariant mass, the rapidity interval spanned by the two jets, the signed
azimuthal angle between the two jets, and the transverse momentum of the
dilepton pair. The data are corrected for the effects of detector inefficiency
and resolution and are sufficiently precise to distinguish between different
state-of-the-art theoretical predictions calculated using Powheg+Pythia8,
Herwig7+Vbfnlo and Sherpa 2.2. The differential cross-sections are used to
search for anomalous weak-boson self-interactions using a dimension-six
effective field theory. The differential cross-section as a function of the
signed azimuthal angle between the two jets is found to be particularly
sensitive to the interference between the Standard Model and dimension-six
scattering amplitudes and provides a direct test of charge-conjugation and
parity invariance in the weak-boson self-interactions.
