Lattice gauge theories in the strong coupling and static limits as a sign-problem-free Ising model

The effective action of the S U (N ) Polyakov-loop model in the strong coupling region and in the static limit for the quark determinant can be mapped onto the Ising model in any dimensions, with the Ising variables attached on the links of the lattice. We use this reformulation to study the finite temperature S U (2 ) lattice gauge theory at finite baryon density.