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

A bstract 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 b 2 , in the θ -expansion of the free energy density around the critical temperature ( T c ) for the confinement-deconfinement transition. Lattice calculations are performed with three different spatial sizes 24 3 , 32 3 , 48 3 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 b 2 much more accurately than the standard full-volume method, and we successfully identify the temperature dependence of b 2 around T c . Our numerical results suggest that the θ -dependence of the free energy density near θ = 0 changes from 4 χ (1 − cos( θ/ 2)) to χ (1 − cos θ ) as the temperature crosses T c .