Phase transitions of a nearest-neighbor Ising-model spin glass

Monte Carlo calculations exhibit a critical point in square $S=\frac{1}{2}$ Ising lattices with random nearest-neighbor interactions, which are distributed according to a Gaussian with mean zero and width $\Delta J$ at $\frac{\Delta J}{k_B{T}_c}\simeq 1.0$. The susceptibility $\chi$ has a cusp there, while the specific heat $C$ has a broad peak with a maximum at somewhat higher temperatures. In nonzero external fields $H$ the cusp of the susceptibility is rounded off, in qualitative agreement with experimental observations. Below $T_c$, hysteresis is found, but the remanent magnetization decays to zero very slowly. Similar nonexponential decay with time is also found for the autocorrelation function $〈{\sigma }_i\mathrm{}\left(0\right)\mathrm{}{\sigma }_i\mathrm{}\left(t\right)\mathrm{}〉$. Some qualitative information on the occurrence of correlated spin clusters and their kinetics is also given.