We consider vector induced lattice gauge theories, in particular we co
nsider the QED induced and we show that at negative temperature corres
ponds to the dimer problem while at positive temperature it describes
a gas of branched polymers with loops. We show that the fermionic mode
ls have D(c) = 6 as upper critical dimension for N not-equal infinity
while the N = infinity model has no upper critical dimension. We also
show that the bosonic models without potential are not critical in the
range of stability of the integral definition of the partition functi
on but they behave as the fermionic models when we analytically contin
ue the free energy.