Instantons in a U(1) lattice gauge theory: A Coulomb dipole gas

We study the decomposition A=A_I+A_SW of a U(1) lattice gauge field into instanton and spin wave parts. The action also decomposes, A=A_I+A_SW+R. Here A_I is a Coulomb dipole gas, A_SW is a zero mass free field, and R is a higher order remainder. We study A_I in detail, for d≧4, in the dilute gas case (which corresponds to the low temperature limit of the gauge field theory). We establish the leading behavior of the free energy:f ∼ e{open}^-daζ. Here e{open} is the lattice spacing, a is a geometrical constant and ζ is an activity defined in terms of a small number of instanton configurations. Our methods suggest the absence of screening in the dilute dipole gas, d≧4, in contrast to Debye screening for the dilute monopole gas.