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Register a new userRoberge-Weiss transition in $N_f=2$ QCD with staggered fermions and $N_tau=6$
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The QCD phase diagram at imaginary chemical potential exhibits a rich structure and studying it can constrain the phase diagram at real values of the chemical potential. Moreover, at imaginary chemical potential standard numerical techniques based on importance sampling can be applied, since no sign problem is present. In the last decade, a first understanding of the QCD phase diagram at purely imaginary chemical potential has been developed, but most of it is so far based on investigations on coarse lattices ($N_tau=4$, $a=0.3:$fm). Considering the $N_f=2$ case, at the Roberge-Weiss critical value of the imaginary chemical potential, the chiral/deconfinement transition is first order for light/heavy quark masses and second order for intermediate values of the mass: there are then two tricritical masses, whose position strongly depends on the lattice spacing and on the discretization. On $N_tau=4$, we have the chiral $m_pi^{text{tric.}}=400:$MeV with unimproved staggered fermions and $m_pi^{text{tric.}}gtrsim900:$MeV with unimproved pure Wilson fermions. Employing finite size scaling we investigate the change of this tricritical point between $N_tau=4$ and $N_tau=6$ as well as between Wilson and staggered discretizations.
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QCD with imaginary chemical potential is free of the sign problem and exhibits a rich phase structure constraining the phase diagram at real chemical potential. We simulate the critical endpoint of the Roberge-Weiss (RW) transition at imaginary chemical potential for $N_text{f}=2$ QCD on $N_tau=6$ lattices with standard Wilson fermions. As found on coarser lattices, the RW endpoint is a triple point connecting the deconfinement/chiral transitions in the heavy/light quark mass regions and changes to a second-order endpoint for intermediate masses. These regimes are separated by two tricritical values of the quark mass, which we determine by extracting the critical exponent $ u$ from a systematic finite size scaling analysis of the Binder cumulant of the imaginary part of the Polyakov loop. We are able to explain a previously observed finite size effect afflicting the scaling of the Binder cumulant in the regime of three-phase coexistence. Compared to $N_tau=4$ lattices, the tricritical masses are shifted towards smaller values. Exploratory results on $N_tau=8$ as well as comparison with staggered simulations suggest that significantly finer lattices are needed before a continuum extrapolation becomes feasible.
In the absence of a genuine solution to the sign problem, lattice studies at imaginary quark chemical potential are an important tool to constrain the QCD phase diagram. We calculate the values of the tricritical quark masses in the Roberge-Weiss plane, $mu=imathpi T/3$, which separate mass regions with chiral and deconfinement phase transitions from the intermediate region, for QCD with $N_text{f}=2$ unimproved staggered quarks on $N_tau=6$ lattices. A quantitative measure for the quality of finite size scaling plots is developed, which significantly reduces the subjective judgement required for fitting. We observe that larger aspect ratios are necessary to unambiguously determine the order of the transition than at $mu=0$. Comparing with previous results from $N_tau=4$ we find a $sim50$% reduction in the light tricritical pion mass. The heavy tricritical pion mass stays roughly the same, but is too heavy to be resolved on $N_tau=6$ lattices and thus equally afflicted with cut-off effects. Further comparison with other discretizations suggests that current cut-off effects on the light critical masses are likely to be larger than $sim100$%, implying a drastic shrinking of the chiral first-order region to possibly zero.
The order of the thermal phase transition in the chiral limit of Quantum Chromodynamics (QCD) with two dynamical flavors of quarks is a long-standing issue and still not known in the continuum limit. Whether the transition is first or second order has important implications for the QCD phase diagram and the existence of a critical endpoint at finite densities. We follow a recently proposed approach to explicitly determine the region of first order chiral transitions at imaginary chemical potential, where it is large enough to be simulated, and extrapolate it to zero chemical potential with known critical exponents. Using unimproved Wilson fermions on coarse $N_t=4$ lattices, the first order region turns out to be so large that no extrapolation is necessary. The critical pion mass $m_pi^capprox 560$ MeV is by nearly a factor 10 larger than the corresponding one using staggered fermions. Our results are in line with investigations of three-flavour QCD using improved Wilson fermions and indicate that the systematic error on the two-flavour chiral transition is still of order 100%.
We have studied the 3-flavor, finite temperature, QCD phase transition with staggred fermions on an $ N_t=4$ lattice. By studying a variety of quark masses we have located the critical point, $m_c$, where the first order 3-flavor transition ends as lying in the region $0.32 le m_c le 0.35$ in lattice units
Overlap fermions are a powerful tool for investigating the chiral and topological structure of the vacuum and the thermal states of QCD. We study various chiral and topological aspects of the finite temperature phase transition of N_f=2 flavours of O(a) improved Wilson fermions, using valence overlap fermions as a probe. Particular emphasis is placed upon the analysis of the spectral density and the localisation properties of the eigenmodes as well as on the local structure of topological charge fluctuations in the vicinity of the chiral phase transition. The calculations are done on 16^3x8 lattices generated by the DIK collaboration.
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