We apply the linear $\delta$ expansion to non-Abelian gauge theory on the lattice, with SU(2) as the gauge group. We establish an appropriate parametrization and evaluate the average plaquette energy $E_P$ to $O\left(\delta \right)$. As a check on our results, we recover the large-$\beta$ expansion up to $O\left(\frac{1}{{\beta }^2}\right)$, which involves some $O\left(\delta \right)$ contributions. Using these contributions we construct a variant of the $\frac{1}{\beta }$ expansion which gives a good fit to the data down to the transition region.

• Received 21 August 1991

DOI:https://doi.org/10.1103/PhysRevD.45.654