The random cluster representation for the infinite-spin Ising model: application to QCD pure gauge theory

Recent advances in high energy QCD experiments probing the deconfinement transition from hadronic to coloured quark matter tend to confirm that perlocation of unbounded quarks could provide a signature of this phase transition. In the strong coupling limit the partition function of SU(2) pure gauge theory can be modeled by that of an infinite spin Ising system with short-range ferromagnetic interactions. We derive the Wolff-random cluster representation for these spin models and show that, at least in these cases, the thermal and geometrical phase transitions indeed coincide. Moreover, our results are presented in a more general setting (e.g., q -states Potts variable and/or long range interactions allowing a generalisation to a variety of physical systems.)