Scaling of magnetic monopoles in the pure compact QED

In the pure U(1) lattice gauge theory with the Villain action we find that the monopole mass in the Coulomb phase and the monopole condensate in the confinement phase scale according to simple power laws. This holds outside the coupling region in which on finite toroidal lattices the metastability phenomena occur. A natural explanation of the observed accuracy of the scaling behaviour would be the second order of the phase transition between both phases in the general space of couplings not far away from the Villain action.