Remarks on the multiparameter reweighting method for the study of lattice QCD at nonzero temperature and density

Abstract

We comment on the reweighting method for the study of finite density lattice QCD. We discuss the applicable parameter range of the reweighting method for models which have more than one simulation parameter. The applicability range is determined by the fluctuations of the modification factor of the Boltzmann weight. In some models having a first order phase transition, the fluctuations are minimized along the phase transition line if we assume that the pressure in the hot and the cold phase is balanced at the first order phase transition point. This suggests that the reweighting method with two parameters is applicable in a wide range for the purpose of tracing out the phase transition line in the parameter space. To confirm the usefulness of the reweighting method for 2 flavor QCD, the fluctuations of the reweighting factor are measured by numerical simulations for the cases of reweighting in the quark mass and chemical potential directions. The relation with the phase transition line is discussed. Moreover, the sign problem caused by the complex phase fluctuations is studied.11.15. Ha, 12.38.Gc, 12.38.Mh

Approach to the thermodynamic limit in lattice QCD atμ≠0

“…[11,16,38,39,40,41,42,43,44,45,46,47]. In this section we compare the one-loop results obtained above to the lattice data of Allton et al [13].…”

The density of states method at non-zero chemical potential

“…The origin of the sign problem are the fluctuations of the complex phase θ, defined by detM ≡ |detM| exp{iθ}. In case those fluctuations ( (θ − θ ) 2 ) become considerably larger than π/2 [2], the problem becomes serious. For a detailed discussion of the phase of the fermion determinant see also [3].…”

The curvature of the critical surface (m_ud,m_s)^{crit}(mu): a progress report

“…When µ = 0, the complex nature of the fermion determinant makes the matter much worse. While finite-µ results, including the location of the QCD critical point, have been obtained by reweighting µ = 0 data [3], assessing the reliability of these results is a challenge in itself [4]. It appears that the only information that can be obtained reliably (i.e.…”