  The Extreme Ultraviolet Imager (EUI) on board the Solar Orbiter (SO)
spacecraft observed small extreme ultraviolet (EUV) bursts, termed campfires,
that have been proposed to be brightenings near the apexes of low-lying loops
in the quiet-Sun atmosphere. The underlying magnetic processes driving these
campfires are not understood. During the cruise phase of SO and at a distance
of 0.523\,AU from the Sun, the Polarimetric and Helioseismic Imager on Solar
Orbiter (SO/PHI) observed a quiet-Sun region jointly with SO/EUI, offering the
possibility to investigate the surface magnetic field dynamics underlying
campfires at a spatial resolution of about 380~km.
  In 71\% of the 38 isolated events, campfires are confined between bipolar
magnetic features, which seem to exhibit signatures of magnetic flux
cancellation. The flux cancellation occurs either between the two main
footpoints, or between one of the footpoints of the loop housing the campfire
and a nearby opposite polarity patch. In one particularly clear-cut case, we
detected the emergence of a small-scale magnetic loop in the internetwork
followed soon afterwards by a campfire brightening adjacent to the location of
the linear polarisation signal in the photosphere, that is to say near where
the apex of the emerging loop lays. The rest of the events were observed over
small scattered magnetic features, which could not be identified as magnetic
footpoints of the campfire hosting loops. The majority of campfires could be
driven by magnetic reconnection triggered at the footpoints, similar to the
physical processes occurring in the burst-like EUV events discussed in the
literature. About a quarter of all analysed campfires, however, are not
associated to such magnetic activity in the photosphere, which implies that
other heating mechanisms are energising these small-scale EUV brightenings.
