We present measurements of the specific heat, magnetization, magnetocaloric effect, and magnetic neutron diffraction carried out on single crystals of antiferromagnetic Yb 3 Pt 4, where highly localized Yb moments order at T N= 2.4 K in zero field. The antiferromagnetic order was suppressed to T N→ 0 by applying a field of 1.85 T in the a b plane. Magnetocaloric effect measurements show that the antiferromagnetic phase transition is always continuous for T N> 0, although a pronounced step in the magnetization is observed at the critical field in both neutron diffraction and magnetization measurements. These steps sharpen with decreasing temperature, but the related divergences in the magnetic susceptibility are cut off at the lowest temperatures, where the phase line itself becomes vertical in the field-temperature plane. As T N→ 0, the antiferromagnetic transition is increasingly influenced by a quantum critical …