  The phase diagram of the quasi two-dimensional antiferromagnet
BaNi$_{2}$V$_{2}$O$_{8}$ is studied by specific heat, thermal expansion,
magnetostriction, and magnetization for magnetic fields applied perpendicular
to $\mathbf{c}$. At $\mu_0H^{*}\simeq1.5$ T, a crossover to a high-field state,
where $T_N(H)$ increases linearly, arises from a competition of intrinsic and
field-induced in-plane anisotropies. The pressure dependences of $T_N$ and
$H^{*}$ are interpreted using the picture of a pressure-induced in-plane
anisotropy. Even at zero field and ambient pressure, in-plane anisotropy cannot
be neglected, which implies deviations from pure
Berezinskii-Kosterlitz-Thouless behavior.

Strongly Correlated Electrons