  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
$\mu_0H^*\simeq2$ T, the N\'eel 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 $T_X\simeq20$ 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.
