Irreversible spin glasses and neural networks

Abstract

We study the way in which the properties of spin glasses and associative memory networks are changed when the interactions between the units are not symmetrical. Our models are analog networks subject to thermal noise (Langevin models). In an approximation which becomes exact in the limit of large spin dimensionality, we find that spin glass phases are suppressed, even for arbitrarily small asymmetry. However, in the associative networks, memory states are not seriously degraded; their critical temperature is simply lowered from its value in the corresponding symmetric model. The effect of making the number of memories a finite fraction of the number of units in the system is also qualitatively the same as in the symmetric case. We suggest that asymmetric couplings may make retrieval of the desired memory states faster, since the system will not get trapped in spin glass states.