We derive an effective cluster model to address the transport properties of
mutually interacting small polarons. We propose a decoupling scheme where the
hopping dynamics of any given particle is determined by separating out
explicitly the degrees of freedom of its environment, which are treated as a
statistical bath. The general cavity method developed here shows that the
long-range Coulomb repulsion between the carriers leads to a net increase of
the thermal activation barrier for electrical transport, and hence to a sizable
reduction of the carrier mobility. A mean-field calculation of this effect is
provided, based on the known correlation functions of the interacting liquid in
two and three dimensions. The present theory gives a natural explanation of
recent experiments performed in organic field-effect transistors with highly
polarizable gate dielectrics, and might well find application in other classes
of polaronic systems such as doped transition-metal oxides