Abstract.A study by specific heat of a polycrystalline sample of the low-dimensional magnetic system Y 2 BaCuO 5 is presented. Magnetic fields up to 14 T are applied and permit to extract the (T ,H) phase diagram. Below µ 0 H * ≃ 2 T, the Néel temperature, associated with a three-dimensional antiferromagnetic long-range ordering, is constant and equals T N = 15.6 K. Above H * , T N increases linearly with H and a field-induced increase of the entropy at T N is related to the presence of an isosbestic point at T X ≃ 20 K, where all the specific heat curves cross. A comparison is made between Y 2 BaCuO 5 and the quasi-two-dimensional magnetic systems BaNi 2 V 2 O 8 , Sr 2 CuO 2 Cl 2 , and Pr 2 CuO 4 , for which very similar phase diagrams have been reported. An effective field-induced magnetic anisotropy is proposed to explain these phase diagrams.