We calculate the effective Polyakov line action corresponding to SU(2) lattice gauge theory on a ${16}^3\times 4$ lattice via the “relative weights” method. We consider a variety of lattice couplings, ranging from $\beta =1.2$ in the strong-coupling domain to $\beta =2.3$ at the deconfinement transition, in order to study how the effective action evolves with $\beta$. Comparison of Polyakov line correlators computed in the effective theory and the underlying gauge theory is used to test the validity of the effective action for $\beta >1.4$, while for $\beta =1.2$, 1.4 we can compare our effective action to the one obtained from a low-order strong-coupling expansion. Very good agreement is found at all couplings. We find that the effective action is given by a simple expression bilinear in the Polyakov lines. The range of the bilinear term, away from strong coupling, grows rapidly in lattice units as $\beta$ increases.

• Received 13 May 2013

DOI:https://doi.org/10.1103/PhysRevD.88.074503