12-16U

Within the framework of the two-particle cluster approximation and the symmetric replica approach, we calculate linear and non-linear ($\sim E^2$, $\sim E^3$) dielectric susceptibilities and construct the $T-x$ phase diagram for a simple proton glass model that takes into account fluctuations of competing short-range and long-range interactions. It is shown that without fluctuations of the internal field the non-linear susceptibilities diverge at $T_0$ (the point where the Edwards-Andersen parameter appears). In presence of the random internal field, the non-linear susceptibility $\sim E^3$ have a rounded peak at $T_0$.