Transition from insulating to a non - insulating temperature dependence of the conductivity in granular metals

We consider interaction effects in a granular normal metal at not very low temperatures. Assuming that all weak localization effects are suppressed by the temperature we replace the initial Hamiltonian by a proper functional of phases and study the possibility for a phase transition depending on the tunneling conductance g. It is demonstrated for any dimension that, while at small g the conductivity decays with temperature exponentially, its temperature dependence is logarithmic at large g. The formulae obtained are compared with an existing experiment and a good agreement is found.