The phase transition by randomly asymmetric bonds

The generalized Hopfield model with randomly asymmetric bonds is studied. It is assumed that the synaptic connections {J_ij} and the external inputs {U_i} contain the "fast noise" and "frozen noise". By averaging over these randomness, we get the kinetic equation of the mean activity with four parameters: means and variances of {U_i} and {J_ij}. This equation has the term of dynamic temperature which is influenced by the mean activity through the variance of {J_ij}. The phase transitions of this system is analyzed. The result of the analysis shows the case that increasing of the randomness induces the transition from a mono-stable state to a bi-stable state, which differs from the ordinary phase transition where only static temperature exists.