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Attempts to extract the order of the chiral transition of QCD at zero chemical potential, with two dynamical flavors of massless quarks, from simulations with progressively decreasing pion mass, have remained inconclusive because of their increasing numerical cost. In an alternative approach to this problem, we consider the path integral as a function of continuous number Nf of degenerate quarks. If the transition in the chiral limit is first order for Nf≥3, a second-order transition for Nf=2 then requires a tricritical point in between. This, in turn, implies tricritical scaling of the critical boundary line between the first-order and crossover regions as the chiral limit is approached. Noninteger numbers of fermion flavors are easily implemented within the staggered fermion discretization. Exploratory simulations at μ=0 and Nf=2.8, 2.6, 2.4, 2.2, 2.1, on coarse Nτ=4 lattices, indeed show a smooth variation of the critical mass mapping out a critical line in the (m, Nf) plane. For the smallest masses, the line appears consistent with tricritical scaling, allowing for an extrapolation to the chiral limit.
The SU(3) pure gauge theory exhibits a first-order thermal deconfinement transition due to spontaneous breaking of its global Z3 center symmetry. When heavy dynamical quarks are added, this symmetry is broken explicitly and the transition weakens with decreasing quark mass until it disappears at a critical point. We compute the critical hopping parameter and the associated pion mass for lattice QCD with Nf=2 degenerate standard Wilson fermions on Nτ∈{6,8,10} lattices, corresponding to lattice spacings a=0.12 fm, a=0.09 fm, a=0.07 fm, respectively. Significant cutoff effects are observed, with the first-order region growing as the lattice gets finer. While current lattices are still too coarse for a continuum extrapolation, we estimate mcπ≈4 GeV with a remaining systematic error of ∼20%. Our results allow us to assess the accuracy of the leading-order and next-to-leading-order hopping expanded fermion determinant used in the literature for various purposes. We also provide a detailed investigation of the statistics required for this type of calculation, which is useful for similar investigations of the chiral transition.