We have applied a multicanonical algorithm in systematic simulations of the Hopfield neural network model, with emphasis on the spin glass region in phase space. All simulations and measurements were done for several storage capacities. Thermodynamic quantities, such as the average energy and specific heat, have been evaluated at all temperatures along with the Edwards-Anderson order parameter. It was observed that, while the purely spin glass region of the model shows a single peak behavior in the specific heat, the mixture region shows either a single or double peak in the specific heat. Also, the Edwards-Anderson order parameter for the purely spin glass region indicated many thermodynamic states at low-temperatures, as expected.