  Matter-free lattice gauge theories (LGTs) provide an ideal setting to
understand confinement to deconfinement transitions at finite temperatures,
which is typically due to the spontaneous breakdown (at large temperatures) of
the centre symmetry associated with the gauge group. Close to the transition,
the relevant degrees of freedom (Polyakov loop) transform under these centre
symmetries, and the effective theory only depends on the Polyakov loop and its
fluctuations. As shown first by Svetitsky and Yaffe, and subsequently verified
numerically, for the $U(1)$ LGT in $(2+1)$-d the transition is in the 2-d XY
universality class, while for the $Z_2$ LGT, it is in the 2-d Ising
universality class. We extend this classic scenario by adding higher charged
matter fields, and show that the notion of universality is generalized such
that the critical exponents $\gamma, \nu$ can change continuously as a coupling
is varied, while their ratio is fixed to the 2-d Ising value. While such weak
universality is well-known for spin models, we demonstrate this for LGTs for
the first time. Using an efficient cluster algorithm, we show that the finite
temperature phase transition of the $U(1)$ quantum link LGT in the spin
$S=\frac{1}{2}$ representation is in the 2-d XY universality class, as
expected. On the addition of $Q = \pm 2e$ charges distributed thermally, we
demonstrate the occurrence of weak universality.
