  Critical phenomenon at the phase transition reveals the universal and
long-distance properties of the criticality. We study the ferromagnetic
criticality of the pyrochlore magnet Lu$_2$V$_2$O$_7$ at the ferromagnetic
transition ${T_\text{c}\approx 70\, \text{K}}$ from the isotherms of
magnetization $M(H)$ via an iteration process and the Kouvel-Fisher method. The
critical exponents associated with the transition are determined as ${\beta =
0.32(1)}$, ${\gamma = 1.41(1)}$, and ${\delta = 5.38}$. The validity of these
critical exponents is further verified by scaling all the $M(H)$ data in the
vicinity of $T_\text{c}$ onto two universal curves in the plot of
$M/|\varepsilon|^\beta$ versus $H/|\varepsilon|^{\beta+\gamma}$, where
${\varepsilon = T/T_\text{c} -1}$. The obtained $\beta$ and $\gamma$ values
show asymmetric behaviors on the ${T < T_\text{c}}$ and the ${T > T_\text{c}}$
sides, and are consistent with the predicted values of 3D Ising and cubic
universality classes, respectively. This makes Lu$_2$V$_2$O$_7$ a rare example
in which the critical behaviors associated with a ferromagnetic transition
belong to different universality classes. We describe the observed criticality
from the Ginzburg-Landau theory with the quartic cubic anisotropy that
microscopically originates from the anti-symmetric Dzyaloshinskii-Moriya
interaction as revealed by recent magnon thermal Hall effect and theoretical
investigations.
