The role of monopoles in the deconfinement transition is discussed in the framework of abelian projection in the maximally abelian gauge in T = 0 SU(2) QCD. Only one (or a few near β c ) long connected monopole loop exists uniformly through the whole lattice in each vacuum configuration in addition to some very short loops in the confinement phase and the long loop disappears in the deep deconfinement region. Energy-entropy balance of the long loops of maximally extended monopoles explains the existence of the deconfinement transition and reproduces roughly the value of the critical temperature
Monopole and photon contributions to abelian Wilson loops are calculated using Monte-Carlo simulations of finite-temperature SU (2) QCD in the maximally abelian gauge. Long monopole loops alone are responsible for the behavior of the string tension in the confinement phase up to the critical β c .Short monopole loops and photons do not contribute to the string tension.The abelian and the monopole spacial string tensions (both of which agree with the normal ones for β < β c ) show a g 4 (T )T 2 scaling behavior in the deconfinement phase. The abelian spacial string tension is in agreement with the full one even in the deconfinement phase. *
Effective monopole actions for various extended monopoles are derived from vacuum configurations after abelian projection in the maximally abelian gauge in T = 0 and T = 0 SU (3) lattice QCD. The actions obtained appear to be independent of the lattice volume adopted. At zero temperature, monopole condensation is seen to occur from energy-entropy balance in the strong coupling region. Larger β is included in the monopole condensed phase as more extended monopoles are considered. The scaling seen in the SU (2) case is not yet observed. The renormalization flow diagram suggests the existence of an infrared fixed point. A hysteresis behavior is seen around the critical temperature in the case of the T = 0 action.
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