  In the theory of antiferromagnetism, the staggered field---an external
magnetic field that alternates in sign on atomic length scales---is used to
select the classical N\'eel state from a quantum magnet, but justification is
missing. This work examines, within the decoherence framework, whether repeated
$local$ measurement can replace a staggered field. Accordingly, the conditions
under which local decoherence can be considered a continuous measurement are
studied. The dynamics of a small magnetic system is analysed to illustrate that
local decoherence can lead to (symmetry-broken) order similar to order
resulting from a staggered field.
