Irreversible Spin Glasses and Neural Networks

We study the way in which the properties of spin glasses and associative memory networks are changed when the interactions between units are not symmetrical. Out models are analog networks subject to thermal noise. In an approximation which becomes exact in the limit of large spin dimensionality, we find that spin glass phases are suppressed, even for small asymmetry. However, in the associative networks, memory states are not seriously degraded; their critical temperature is simply changed from its value in the corresponding symmetric model. We suggest that asymmetric couplings may take retrieval of the desired memory states faster, since the system will not get trapped in spin glass states.