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We report on the status of ongoing investigations aiming at locating the deconfinement critical point with standard Wilson fermions and Nf = 2 flavors towards the continuum limit (standard Columbia plot); locating the tricritical masses at imaginary chemical potential with unimproved staggered fermions at Nf = 2 (extended Columbia plot); identifying the order of the chiral phase transition at μ = 0 for Nf = 2 via extrapolation from non integer Nf (alternative Columbia plot).

In this contribution we report the status and plans of the open lattice initiative to generate and share new gauge ensembles using the stabilised Wilson fermion framework. The production strategy is presented in terms of a three stage plan alongside summaries of the data management as well as access policies. Current progress in completing the first stage of generating ensembles at four lattice spacings at the flavor symmetric point is given.

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.

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 OpenLat initiative presents its results of lattice QCD simulations using Stabilized Wilson Fermions (SWF) using 2+1 quark flavors. Focusing on the SU(3) flavor symmetric point mπ=mK=412 MeV, four different lattice spacings (a=0.064,0.077,0.094,0.12 fm) are used to perform the continuum limit to study cutoff effects. We present results on light hadron masses; for the determination we use a Bayesian analysis framework with constraints and model averaging to minimize the bias in the analysis.

Phase transitions in a non-perturbative regime can be studied by ab initio Lattice Field Theory methods. The status and future research directions for LFT investigations of Quantum Chromo-Dynamics under extreme conditions are reviewed, including properties of hadrons and of the hypothesized QCD axion as inferred from QCD topology in different phases. We discuss phase transitions in strong interactions in an extended parameter space, and the possibility of model building for Dark Matter and Electro-Weak Symmetry Breaking. Methodological challenges are addressed as well, including new developments in Artificial Intelligence geared towards the identification of different phases and transitions.

The nature of the QCD chiral phase transition in the limit of vanishing quark masses has remained elusive for a long time, since it cannot be simulated directly on the lattice and is strongly cutoff-dependent. We report on a comprehensive ongoing study using unimproved staggered fermions with Nf ∈ [2, 8] mass-degenerate flavours on Nτ ∈ {4, 6, 8} lattices, in which we locate the chiral critical surface separating regions with first-order transitions from crossover regions in the bare parameter space of the lattice theory. Employing the fact that it terminates in a tricritical line, this surface can be extrapolated to the chiral limit using tricritical scaling with known exponents. Knowing the order of the transitions in the lattice parameter space, conclusions for approaching the continuum chiral limit in the proper order can be drawn. While a narrow first-order region cannot be ruled out, we find initial evidence consistent with a second-order chiral transition in all massless theories with Nf ≤ 6, and possibly up to the onset of the conformal window at 9 ≲ N∗f ≲ 12. A reanalysis of already published O(a)-improved Nf = 3 Wilson data on Nτ ∈ [4, 12] is also consistent with tricritical scaling, and the associated change from first to second-order on the way to the continuum chiral limit. We discuss a modified Columbia plot and a phase diagram for many-flavour QCD that reflect these possible features.

n this joint contribution we announce the formation of the "OPEN LATtice initiative", this https URL, to study Stabilised Wilson Fermions (SWF). They are a new avenue for QCD calculations with Wilson-type fermions and we report results on our continued study of this framework: Tuning the clover improvement coefficient, and extending the reach of lattice spacings to a=0.12 fm. We fix the flavor symmetric points mπ=mK=412 MeV at a=0.055,0.064,0.077,0.094,0.12 fm and define the trajectories to the physical point by fixing the trace of the quark mass matrix. Currently our pion mass range extends down to mπ∼200 MeV. We outline our tuning goals and strategy as well as our future planned ensembles. First scaling studies are performed on fπ and mπ. Additionally results of a preliminary continuum extrapolation of mN at the flavor symmetric point are presented. Going further a first determination of the light and strange hadron spectrum chiral dependence is shown, which serves to check the quality of the action for precision measurements. We also investigate other quantities such as flowed gauge observables to study how the continuum limit is approached. Taken together we observe the SWF enable us to perform stable lattice simulations across a large range of parameters in mass, volume and lattice spacing. Pooling resources our new initiative has made our reported progress possible and through it we will share generated gauge ensembles under an open science philosophy.