Composite reweighting the Glasgow method for finite density QCD

Crompton, P. R.

doi:10.1016/s0550-3213(01)00519-3

Cited by 18 publications

(21 citation statements)

References 24 publications

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“…The Glasgow method [7] is one of the reweighting methods. A composite (Glasgow) reweighting method has recently been proposed by [8]. Another approach is analytic continuation from simulations at imaginary chemical potential [9][10][11].…”

Section: Introductionmentioning

confidence: 99%

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

Ejiri

2004

Phys. Rev. D

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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

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Section: Introductionmentioning

confidence: 99%

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

Ejiri

2004

Phys. Rev. D

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“…Often, this roundoff restricts the range of lattice volumes that can be treated via an approach involving diagonalization. To address this problem in our analysis, we have implemented the tested techniques in [22] designed to minimise roundoff. These techniques involve using Newton's relations to define the operation…”

Section: This a General Problem For All Exact Diagonalization And Denmentioning

confidence: 99%

“…What this means is that the Von Neumann entropy in (22) then has a well defined asymptotic limit as a function of any finite local degree of freedom M, such as lattice system size, since the normalizing conditions in (14) guarantee the convexity of the above functional [35].…”

Section: A the Zeroes Density Of The Ising Modelmentioning

confidence: 99%

“…Specifically, it is the regularized local limit of the more usual Von Neumann entropy in (22), defined via a ζ-function renormalization prescription [34][35] [36]. To obtain (19) we have considered the continuous-J limit of the lattice partition function in (6), in which the local transition probabilities λ i become a continuous function of J, given by λ(β, J).…”

Section: Entanglement Entropymentioning

confidence: 99%

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The partition function zeroes of quantum critical points

Crompton¹

2009

Nuclear Physics B

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The Lee-Yang theorem for the zeroes of the partition function is not strictly applicable to quantum systems because the zeroes are defined in units of the fugacity e h∆τ , and the Euclidean-time lattice spacing ∆τ can be divergent in the infrared (IR). We recently presented analytic arguments describing how a new space-Euclidean time zeroes expansion can be defined, which reproduces Lee and Yang's scaling but avoids the unresolved branch points associated with the breaking of nonlocal symmetries such as parity. We now present a first numerical analysis for this new zeros approach for a quantum spin chain system. We use our scheme to quantify the renormalization group flow of the physical lattice couplings to the IR fixed point of this system. We argue that the generic Finite-Size Scaling (FSS) function of our scheme is identically the entanglement entropy of the lattice partition function and, therefore, that we are able to directly extract the central charge, c, of the quantum spin chain system using conformal predictions for the scaling of the entanglement entropy.

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“…The method seems mature for quantitative studies in realistic cases, and a nice possibility is offered by a combination of this approach with other methods, for instance by using reweighting [9] [7] or direct calculations of derivatives [11] at nonzero µ to improve the accuracy of the results at negative µ 2 . Finally, the study of discontinuities as sketched in Sect.3 above might offer an alternative approach to the study of the endpoints and tricritical points.…”

Section: Summary/outlookmentioning

confidence: 99%

QCD critical region and quark gluon plasma from an imaginary μB

D’Elia¹,

Lombardo²

2004

Nuclear Physics B - Proceedings Supplements

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We discuss the imaginary chemical potential approach to the study of QCD at nonzero temperature and density, present results for the four flavor model in the different phases and show that this method is ideally suited for a comparison between lattice data and phenomenological models. QCD and a complex µ BResults from simulations with an imaginary chemical potential can be analytically continued to a real chemical potential, thus circumventing the sign problem [1], [2] [3]. In practice, the analytical continuation is carried out along one line in the complex µ plane: first along the imaginary axes, and then along the real one. It is then meaningful to map this path in the complex µ 2 plane: because of the symmetry property Z(µ) = Z(−µ) this can be achieved without losing generality. In the complex µ 2 plane the partition function is real for real values of the external parameter µ 2 , complex otherwise: the situation resembles that of ordinary statistical models in an external field. Hence, the analyticity of the physical observables [4] as well as that of the critical line [2] follows naturally.The phase diagram in the temperature, (real) µ 2 plane is sketched in Fig.1, where we omit the superconducting and the color flavor locked phase, which (unfortunately) play no rôle in our discussion. The region accessible to numerical simulations is the one with µ 2 ≤ 0: at a variance with other approaches to finite density QCD which only use information at µ = 0 [5] [6] [7] the imaginary chemical potential method exploits the entire halfspace. And we will also argue that there are physical questions which can be addressed without analytic continuation. * Electronic address: delia@ge.infn.it † Electronic address: lombardo@lnf.infn.it It encodes reality for real µ 2 , contains the physical scale T c , is dimensionally consistent, gives T (µ = 0) = T c , T (µ = 0) < T c . We refer to Section IV of Ref.[3] for our results on the critical line in the four flavor model, and their discussion in terms of model calculations. Here it suffices to remind ourselves that the second order approx-

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Composite reweighting the Glasgow method for finite density QCD

Cited by 18 publications

References 24 publications

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

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

The partition function zeroes of quantum critical points

QCD critical region and quark gluon plasma from an imaginary μB

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