Annealing Dynamics of the Two-Dimensional Fully Frustrated Ising Model

We study the dynamical scaling properties of the two-dimensional fully frustrated Ising model by simulated annealing. The model has a highly degenerate, critical ground state with well known equilibrium properties. To study its out-of-equilibrium behavior, we develop an annealing protocol that is convenient for extending the Kibble-Zurek mechanism to the case of an exponentially divergent correlation length in the limit of the temperature $T\to T_c=0$. We find excellent agreement with the scaling forms derived, including a dependence on the initial temperature that is not present in the conventional Kibble-Zurek mechanism. The dynamic exponent $z$ is consistent among all quantities studied; fits of its dependence on the initial temperature give $z=1.99(2)$ (susceptibility), $z=2.072(8)$ (excess energy), and $z=2.09(3)$ (Edwards-Anderson order parameter). These values are close to $z=2$, which is consistent with previous studies of relaxation after instantaneous quenches and of time dependent correlations in equilibrium, including the estimate $z=2.004(9)$ from equilibrium autocorrelation functions.