Effect of stout smearing on the phase diagram from multiparameter reweighting in lattice QCD

Abstract

The phase diagram and the location of the critical endpoint (CEP) of lattice QCD with unimproved staggered fermions on a Nt = 4 lattice was determined fifteen years ago with the multiparameter reweighting method by studying Fisher zeros. We first reproduce the old result with an exact algorithm (not known at the time) and with statistics larger by an order of magnitude. As an extension of the old analysis we introduce stout smearing in the fermion action in order to reduce the finite lattice spacing effects. First we show that increasing the smearing parameter ρ the crossover at µ = 0 gets weaker, i.e., the leading Fisher zero gets farther away from the real axis. Furthermore as the chemical potential is increased the overlap problem gets severe sooner than in the unimproved case, therefore shrinking the range of applicability of the method. Nevertheless certain qualitative features remain, even after introducing the smearing. Namely, at small chemical potentials the Fisher zeros first get farther away from the real axis and later at around aµq = 0.1 − 0.15 they start to get closer, i.e., the crossover first gets weaker and later stronger as a function of µ. However, because of the more severe overlap problem the CEP is out of reach with the smeared action.

New approach to lattice QCD at finite density; results for the critical end point on coarse lattices

“…More precisely, the infinite volume extrapolated result shows that the imaginary part of the leading Fisher zero is more or less flat up to aµ ∼ 0.15 and a sharp decrease is observed for 0.15 ≤ aµ ≤ 0.2. The observed flatness agrees within errors with the slight increase seen in [42,59], and cannot be significantly distinguished from it with the currently available statistics. This means that in the range of chemical potentials where our results are reliable with trustworthy statistical errors, i.e., ε abs,µ = 0, we are able to conclude with high statistical significance that the leading singularity of log Z is eventually moving closer and closer to the real axis.…”

“…At each µ and spatial volume the bare coupling was set to β c as follows. For each µ, initial β c0 values were taken from [59]. The leading Fisher zeros (see section 3.2), β 1 + iβ 2 were measured in shorter runs and β c0 was modified by ∆β = β 1 − β c0 if necessary.…”

“…The resulting values are shown in table 1. From [59] we also glean that the spatial volume dependence of β c is rather mild and in this first exploratory work we set the same bare coupling for all of our 3 spatial volumes.…”

On the order of the QCD chiral phase transition for different numbers of quark flavours

“…One would expect an effect similar to that of decreasing the lattice spacing. Indeed, such an effect was observed in an earlier study with a stoutsmeared staggered action for N f = 3 at µ = 0 [48], and more recently for N f = 2 + 1 at the physical point [49]. In particular, also the tricritical boundary line in figure 9 should then shift upwards, while its left end should remain anchored at the conformal point.…”

Lattice simulations of the QCD chiral transition at real $μ_B$

“…It was actually demonstrated in Ref. [25], that the main bottleneck in extending such studies to finer lattices is the overlap problem in the weights w t /w s , which becomes severe already at moderate chemical potentials, where the sign problem is still numerically manageable. This overlap problem in the weights w t /w s is not present if they take values in a compact space.…”