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

Abstract

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 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 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 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 4χ(1 − cos(θ/2)) to χ(1 − cos θ) as the temperature crosses T c .

Keywords

• Algorithms and Theoretical Developments
• Non-Zero Temperature and Density
• Phase Transitions