Two Information Entropies of Square-Lattice $\pm {J}$ Ising Models

Two information entropies, $S_{IB}$ based on the local bonding energy configurations and $S_{IS}$ based on the local spin configurations, are applied in the square-lattice $\pm {J}$ Ising systems with Monte Carlo simulations. With $S_{IB}$ and $S_{IS}$, the spin glass states can be distinguished from paramagnetic states clearly. The results reveal that the nature of spin glass states is of ordering in bonding energy and disordering in spin orientations. The consistence of $S_{IB}$ and the thermodynamic entropy is found.