  The region near a critical point is studied using holographic models of
second-order phase transitions. In a previous paper, we argued that the quantum
circuit complexity of the vacuum ($C_0$) is the largest at the critical point.
When deforming away from the critical point by a term $\int d^d x \, \tau \,
O_\Delta$ the complexity $C(\tau)$ has a piece non-analytic in $\tau$, namely
$C_0 -C(\tau) \sim |\tau-\tau_c|^{\nu(d-1)} + \mathrm{analytic} $. Here, as
usual, $\nu=\frac{1}{d-\Delta}$ and $\xi$ is the correlation length $\xi\sim
|\tau-\tau_c|^{-\nu}$ and there are possible logarithmic corrections to this
expression. That was derived using numerical results for the Bose-Hubbard model
and general scaling considerations. In this paper, we show that the same is
valid in the case of holographic complexity providing evidence that the results
are universal, and at the same time providing evidence for holographic
computations of complexity.
