We discuss the nature of symmetry breaking in quantum antiferromagnets. We show that published arguments concerning the order parameter for the 2d s =1/2 Heisenberg antiferromagnet have to be reconsidered. These had led to 3‾√3textbackslashsqrt3 and 1 for the ratio r of the mean z -component m of the staggered spin per particle m s z in an infinitesimal staggered field B , to the r.m.s. value m 0 of m s z with B =0, in the thermodynamic limit. We give arguments which put doubt on both values. Also we prove r ≧1, given m 0 ≠0.