Nonequilibrium critical dynamics of the two-dimensional $\pm J$ Ising model

Abstract: 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.