Universality of deconfining phase transition in (3+1)-dimensional SU(2) lattice gauge theory

The (3+1)-dimensional SU(2) lattice gauge theory at finite temperature is studied by Monte Carlo renormalization-group methods on a ${32}^3$×${\mathrm{N}}_{\mathrm{t}}$ lattice with ${\mathrm{N}}_{\mathrm{t}}$=2 and 4. It is shown that the effective theory of the Polyakov loop has only short-range couplings and that the deconfining phase transition is governed by the same fixed point and critical indices as the three-dimensional Ising model, thus proving that the two theories belong to the same universality class.