  We use Monte Carlo (MC) methods to simulate a two-dimensional (2D)
bond-diluted Ising model on the square lattice which has frustration between
the nearest-neighbor interaction J1 and the next-nearest-neighbor interaction
J2. In this paper, we use the parallel tempering algorithm to study the
thermodynamics for different diluted ratio x and give the phase diagram. The
presence of both frustration and disorder results in a spin-glass phase, which
exists between the stripe antiferromagnetic phase and the Neel phase. We
present the ground-state energy of T -> 0 and the size-dependence of
Edwards-Anderson (EA) order parameter for the spin glass phase. By scaling the
mean energy and the EA order parameter from the simulated annealing with the
Kibble-Zurek (KZ) mechanism, we obtain two different dynamic exponents z_E and
z_q for the spin glass phase. Experimentally, this model has close implication
with the FeAs plane of the iron-based superconductor BaFe2(As(1-x)P(x))2, where
a spin-glass like phase was found.
