Finite Size Scaling Study of the Deconfining Phase Transition in Pure SU(3) Lattice Gauge Theory

Abstract Finite-size scaling behavior is studied for the deconfining phase transition of the pure SU(3) gauge theory on a lattice with size varying from 8 3 × 4 to 28 3 × 4. It is shown that the critical behavior of various susceptibilities exhibits finite-size scaling linear in the spatial volume quite accurately and that a cumulant taken as an indicator of the order of transition shows a behavior anticipated for a first-order transition. It is also found that the mass derived from the unsubtracted correlation function has a conspicuous volume dependence characteristic of a first-order phase transition. Furthermore, the physical mass gap representing a single particle excitation is shown to stay at a finite value at the transition point. We also demonstrate that the deconfining phase transition is controlled by the Z(3) property of Polyakov lines, their magnitude and phase fluctuations around the Z(3)-axes being unimportant, and that the effective Z(3) action possesses positive two-spin couplings which decrease exponentially with the distance between the two spins. All this evidence supports the first-order nature of the deconfining transition of the pure SU(3) gauge theory.

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