The Kentucky noisy Monte Carlo algorithm for Wilson dynamical fermions

Joó, Bálint; Horváth, I.; Liu, K. F.

doi:10.1103/physrevd.67.074505

Cited by 10 publications

(5 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We note that the accept/reject step is designed to be based on the determinant ratio which has been shown to alleviate the fluctuation problem [23,26,42] and enhance the acceptance rate.…”

Section: A Canonical Partition Functionmentioning

confidence: 99%

See 1 more Smart Citation

Finite density phase transition of QCD withNf=4andNf=2using canonical ensemble method

Alexandru

Liu

et al. 2010

Phys. Rev. D

View full text Add to dashboard Cite

In a progress toward searching for the QCD critical point, we study the finite density phase transition of N f = 4 and 2 lattice QCD at finite temperature with the canonical ensemble approach.We develop a winding number expansion method to accurately project out the particle number from the fermion determinant which greatly extends the applicable range of baryon number sectors to make the study feasible. Our lattice simulation was carried out with the clover fermions and improved gauge action. For a given temperature, we calculate the baryon chemical potential from the canonical approach to look for the mixed phase as a signal for the first order phase transition.In the case of N f = 4, we observe an "S-shape" structure in the chemical potential-density plane due to the surface tension of the mixed phase in a finite volume which is a signal for the first order phase transition. We use the Maxwell construction to determine the phase boundaries for three temperatures below T c . The intersecting point of the two extrapolated boundaries turns out to be at the expected first order transition point at T c with µ = 0. This serves as a check for our method of identifying the critical point. We also studied the N f = 2 case, but do not see a signal of the mixed phase for temperature as low as 0.83 T c .

show abstract

“…We note that the accept/reject step is designed to be based on the determinant ratio which has been shown to alleviate the fluctuation problem [23,26,42] and enhance the acceptance rate.…”

Section: A Canonical Partition Functionmentioning

confidence: 99%

“…Although the matrix is very sparse, exact determinant calculation is very demanding even on this small lattice. An alternative is to use a noisy estimator [28,42].…”

Section: B Winding Number Expansionmentioning

confidence: 99%

Finite density phase transition of QCD withNf=4andNf=2using canonical ensemble method

Alexandru

Liu

et al. 2010

Phys. Rev. D

View full text Add to dashboard Cite

show abstract

“…A noisy Monte Carlo algorithm [17] with Padé-Z 2 estimates [18,19] of the T r log of the fermion matrix are developed toward this goal and a numerical simulation with Wilson dynamical fermion is carried out [20]. We shall summarize the progress made so far.…”

Section: Noisy Monte Carlo With Fermion Determinantmentioning

confidence: 99%

“…the following two steps are needed to prove detailed balance [17,20]. (a) Let T 1 (U, U ′ ) be the ergodic Markov matrix satisfying detailed balance with respect to P 1 , in other words P 1 (U )T 1 (U, U ′ )dU = P 1 (U ′ )T 1 (U ′ , U )dU ′ .…”

Section: Noisy Monte Carlo With Fermion Determinantmentioning

confidence: 99%

“…The noisy Monte Carlo algorithm has been implemented for the Wilson dynamical fermion with pure gauge update (Kentucky Noisy Monte Carlo Algorithm) for an 8 4 lattice with β = 5.5 and κ = 0.155 [20]. Several tricks are employed to reduce the fluctuations of the T r ln M estimate and increase the acceptance.…”

Section: Implementation Of the Noisy Monte Carlo Algorithmmentioning

confidence: 99%

See 1 more Smart Citation

A Finite Baryon Density Algorithm

Liu

Lecture Notes in Computational Science and Engineering

View full text Add to dashboard Cite

⋆⋆I will review the progress toward a finite baryon density algorithm in the canonical ensemble approach which entails particle number projection from the fermion determinant. These include an efficient Padé-Z 2 stochastic estimator of the T r log of the fermion matrix and a Noisy Monte Carlo update to accommodate unbiased estimate of the probability. Finally, I will propose a Hybrid Noisy Monte Carlo algorithm to reduce the large fluctuation in the estimated T r log due to the gauge field which should improve the acceptance rate. Other application such as treating u and d as two separate flavors is discussed.

show abstract