Transition from exponential to a power law 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 depends on temperature exponentially, it obeys a power law at large $g$. The exponent is estimated for an existing experiment and a good agreement is found.