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 c onfinement phase scale according to simple power laws. This holds outside t he coupling region in which on finite toroidal lattices the metastability p henomena occur. A natural explanation of the observed accuracy of the scali ng 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 act ion.