  The $\pm J$ Ising model is a simple frustrated spin model, where the exchange
couplings independently take the discrete value $-J$ with probability $p$ and
$+J$ with probability $1-p$. It is especially appealing due to its connection
to quantum error correcting codes. Here, we investigate the nonequilibrium
critical behavior of the two-dimensional $\pm J$ Ising model, after a quench
from different initial conditions to a critical point $T_c(p)$ on the
paramagnetic-ferromagnetic (PF) transition line, especially, above, below and
at the multicritical Nishimori point (NP). The dynamical critical exponent
$z_c$ seems to exhibit non-universal behavior for quenches above and below the
NP, which is identified as a pre-asymptotic feature due to the repulsive fixed
point at the NP. Whereas, for a quench directly to the NP, the dynamics reaches
the asymptotic regime with $z_c \simeq 6.02(6)$. We also consider the
geometrical spin clusters (of like spin signs) during the critical dynamics.
Each universality class on the PF line is uniquely characterized by the
stochastic Loewner evolution (SLE) with corresponding parameter $\kappa$.
Moreover, for the critical quenches from the paramagnetic phase, the model,
irrespective of the frustration, exhibits an emergent critical percolation
topology at the large length scales.

Statistical Mechanics;Quantum Physics