Antiferromagnetic order without recourse to staggered fields

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.