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

We apply the previously-developed sub-volume method to study the θ-dependence of the four-dimensional SU(2) Yang-Mills theory. 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 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 sub-volume method allows us to determine the values of b_2 much more accurately than the standard full-volume method, and we have successfully measured the temperature dependence of b_2 around the critical temperature. Our numerical results suggest that the θ-dependence of the free energy density changes approximately from 4χ(1-cos(θ/2)) to χ(1-cosθ) near θ=0 as the temperature increases.