Subvolume method for SU(2) Yang-Mills theory at finite temperature: topological charge distributions

Abstract

We apply the previously-developed sub-volume method to study the θ-dependence of the four-dimensional SU(2) Yang-Mills theory at finite temperature. We calculate the first two coefficients, the topological susceptibility χ and the fourth cumulant b2, in the θ-expansion of the free energy density around the critical temperature (Tc) for the confinement-deconfinement transition. Lattice calculations are performed with three different spatial sizes 243, 323, 483 to monitor finite size effects, while the temporal size is fixed to be 8. The systematic uncertainty associated with the sub-volume extrapolation is studied with special care. The sub-volume method allows us to determine the values of b2 much more accurately than the standard full-volume method, and we successfully identify the temperature dependence of b2 around Tc. Our numerical results suggest that the θ-dependence of the free energy density near θ = 0 changes from 4χ(1 − cos(θ/2)) to χ(1 − cos θ) as the temperature crosses Tc.