Deconfinement phase transition in one-flavor QCD

We present a study of the deconfinement phase transition of one-flavor QCD using the multiboson algorithm. The mass of the Wilson fermions relevant for this study is moderately large and the non-Hermitian multiboson method is a superior simulation algorithm. Finite-size scaling is studied on lattices of size $8^3\times 4,$ ${12}^3\times 4$, and ${16}^3\times 4$. The behaviors of the peak of the Polyakov loop susceptibility, the deconfinement ratio, and the distribution of the norm of the Polyakov loop are all characteristic of a first-order phase transition for heavy quarks. As the quark mass decreases, the first-order transition gets weaker and turns into a crossover. To investigate finite-size scaling on larger spatial lattices we use an effective action in the same universality class as QCD. This effective action is constructed by replacing the fermionic determinant with the Polyakov loop identified as the most relevant $Z\left(3\right)\mathrm{}$-symmetry-breaking term. Higher-order effects are incorporated in an effective $Z\left(3\right)\mathrm{}$-breaking field h, which couples to the Polyakov loop. Finite-size scaling determines the value of h where the first-order transition ends. Our analysis at the end point $h_{\mathrm{ep}}$ indicates that the effective model and thus QCD are consistent with the universality class of the three-dimensional Ising model. Matching the field strength at the end point $h_{\mathrm{ep}}$ to the $\kappa$ values used in the dynamical quark simulations we estimate the end point ${\kappa }_{\mathrm{ep}}$ of the first-order phase transition. We find ${\kappa }_{\mathrm{ep}}\sim 0.08$ which corresponds to a quark mass of about 1.4 GeV.