Percolation renormalization group analysis of confinement in Z2 lattice gauge theories

The analytical study of confinement in lattice gauge theories (LGTs) remains a difficult task to this day. Taking a geometric perspective on confinement, we develop a real-space renormalization group (RG) formalism for Z(2) LGTs using percolation probability as a confinement order parameter. The RG flow we analyze is constituted by both the percolation probability and the coupling parameters. We consider a classical Z(2) LGT in two dimensions, with matter and thermal fluctuations, and analytically derive the confinement phase diagram. We find good agreement with numerical and exact benchmark results and confirm that a finite matter density enforces confinement at T < infinity in the model we consider. Our RG scheme enables future analytical studies of Z(2) LGTs with matter and quantum fluctuations and beyond.