  Some time ago, Svetitsky and Yaffe have argued that -- if the deconfinement
phase transition of a (d+1)-dimensional Yang-Mills theory with gauge group G is
second order -- it should be in the universality class of a d-dimensional spin
model symmetric under the center of G. For d=3 these arguments have been
confirmed numerically only in the SU(2) case with center Z(2), simply because
all SU(N) Yang-Mills theories with N>=3 seem to have non-universal first order
phase transitions. The symplectic groups Sp(N) also have the center Z(2) and
provide another extension of SU(2) = Sp(1) to general N. Using lattice
simulations, we find that the deconfinement phase transition of Sp(2)
Yang-Mills theory is first order in 3+1 dimensions, while in 2+1 dimensions
stronger fluctuations induce a second order transition. In agreement with the
Svetitsky-Yaffe conjecture, for (2+1)-d Sp(2) Yang-Mills theory we find the
universal critical behavior of the 2-d Ising model. For Sp(3) Yang-Mills theory
the transition is first order both in 2+1 and in 3+1 dimensions. This suggests
that the size of the gauge group -- and not the center symmetry -- determines
the order of the deconfinement phase transition.
