Magnetic Ordering in Cerium Monochalcogenides: A Test Case forεExpansions withn=4

CeSe and CeTe are found by neutron diffraction to be type-II antiferromagnets with the moment along the propagation vector. The phase transitions are continuous with the critical exponent for the magnetization $\beta =0.36\mathrm{}\pm 0.02$. This constitutes a violation of the $\epsilon$-expansion predictions of Bak, Krinsky, and Mukamel, which hitherto have been successfully applied to a number of $n>~4$ systems and according to which the transitions should be of first order.