Abelian lattice gauge theories in 3 + 1 dimensions: The linked cluster approach

We use the linked cluster expansion methods of Nickel to derive strong couping series for Z_N abelian gauge theories. These new results together with corresponding estimates using the exact linked cluster expansion algorithm are analysed and compared with previously obtained results for U(1) lattice gauge theory in 3 + 1 dimensions. We confirm the phase structure of these theories as found by other techniques. The critical value of N at which the phase structure of Z_N alters is estimated to be N_C = 4.5 ± 0.2. In each case the string tension estimates using the ELCE algorithm are found to be stable in the presence of a roughening transition.