The deconfinement phase transition of Sp(2) and Sp(3) Yang-Mills theories in 2+1 and 3+1 dimensions

摘要

Some time ago, Svetitsky and Yaffe have argued that-if the deconfinement phase transition of a (d + I)-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 greater than or equal to 3 seem to have nonuniversal first order phase transitions. The symplectic groups Sp(N) also have the center Z(2) and provide another extension of SU(2) = Sp(l) to general N. Using lattice simulations, we find that the deconfinement phase transition of Sp(2) Yang-Mills theory is first order in 3 + I dimensions, while in 2 + I dimensions stronger fluctuations induce a second order transition. In agreement with the Svetitsky-Yaffe conjecture, for (2 + I)d Sp(2) Yang-Mills theory we find the universal critical behavior of the 2d Ising model. For Sp(3) Yang-Mills theory the transition is first order both in 2 + I and in 3 + I dimensions. This suggests that the size of the gauge group-and not the center symmetry-determines the order of the deconfinement phase transition. (C) 2004 Elsevier B.V. All rights reserved.