We use Monte Carlo (MC) methods to simulate a two-dimensional (2D) bond-diluted Ising model on the square lattice, which has frustration between nearest-neighbor interaction $J_1$ and next-nearest-neighbor interaction $J_2$. In this study, we use the parallel tempering algorithm to study thermodynamics for different diluted ratios $x$ [where $x=N{\left(J_2\right)}_{\mathrm{diluted}}/2N$, where $N$ denotes the system volume] and present a phase diagram. The presence of frustration and disorder results in a spin-glass phase, which exists between the stripe antiferromagnetic phase and Néel phase. We present a ground-state energy of $T\to 0$ and the size dependence of the Edwards-Anderson (EA) order parameter for the spin-glass phase. By scaling the mean energy and EA order parameter from the simulated annealing with the Kibble-Zurek mechanism, we obtain two different dynamic exponents, $z_E$ and $z_q$, for the spin-glass phase. Experimentally, this model has a close relationship with the $\mathrm{FeAs}$ plane of the iron-based superconductor ${\mathrm{BaFe}}_2{\left({\mathrm{As}}_{1-x}{\mathrm{P}}_x\right)}_2$, where a spin-glass-like phase was found.

• Received 29 December 2017

DOI:https://doi.org/10.1103/PhysRevB.97.224419