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<p>We present an exploratory study to determine the confinement-deconfinement transition temperature at finite <i>θ</i>, <i>T</i><sub><i>c</i></sub>(<i>θ</i>), for the 4d SU(2) pure Yang-Mills theory. Lattice numerical simulations are performed on three spatial sizes <i>N</i><sub><i>S</i></sub> = 24, 32, 48 with a fixed temporal size <i>N</i><sub><i>T</i></sub> = 8. We introduce a non-zero <i>θ</i>-angle by the sub-volume method to mitigate the sign problem. By taking advantage of the universality in the second order phase transition and the Binder cumulant of the order parameter, the <i>θ</i>-dependence of <i>T</i><sub><i>c</i></sub> is determined to be <i>T</i><sub><i>c</i></sub>(<i>θ</i>)/<i>T</i><sub><i>c</i></sub>(0) = 1 <i>−</i> 0<i>.</i>16(2) (<i>θ</i>/<i>π</i>)<sup>2</sup> − 0<i>.</i>03(4) (<i>θ</i>/<i>π</i>)<sup>4</sup> up to <i>θ</i> ∼ 0.9 <i>π</i>. The reliability of the extrapolations in the sub-volume method is extensively checked. We also point out that the temperature dependence of the topological susceptibility should exhibit a singularity with the exponent for the specific heat.</p>

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θ dependence of Tc in SU(2) Yang-Mills theory

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  • 发表日期：

    2025年2月28日

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  • Norikazu Yamada,
  • Masahito Yamazaki,
  • Ryuichiro Kitano

摘要

We present an exploratory study to determine the confinement-deconfinement transition temperature at finite θ, Tc(θ), for the 4d SU(2) pure Yang-Mills theory. Lattice numerical simulations are performed on three spatial sizes NS = 24, 32, 48 with a fixed temporal size NT = 8. We introduce a non-zero θ-angle by the sub-volume method to mitigate the sign problem. By taking advantage of the universality in the second order phase transition and the Binder cumulant of the order parameter, the θ-dependence of Tc is determined to be Tc(θ)/Tc(0) = 1 − 0.16(2) (θ/π)2 − 0.03(4) (θ/π)4 up to θ ∼ 0.9 π. The reliability of the extrapolations in the sub-volume method is extensively checked. We also point out that the temperature dependence of the topological susceptibility should exhibit a singularity with the exponent for the specific heat.