Volume dependence of the pion mass in the quark-meson model

Braun, Jens; Klein, Bertram; Pirner, Hans J.

doi:10.1103/physrevd.71.014032

Cited by 66 publications

(124 citation statements)

References 33 publications

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“…This will be explored in future work. We wish to note, however, that negative values for R[M π ] have also been observed in the quark meson model for unequal spatial and temporal box lengths, see [16,17] for details.…”

Section: Numerical Resultsmentioning

confidence: 99%

Volume behavior of quark condensate, pion mass, and decay constant from Dyson-Schwinger equations

2010

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We solve the coupled system of Dyson-Schwinger and Bethe-Salpeter equations for the quark propagator and the pion Bethe-Salpeter amplitude on a finite volume. To this end we use a truncation scheme that includes pion cloud effects in the quark propagator and light mesons. We study volume effects in the quark condensate, the pion mass and the pion decay constant and compare to corresponding results in other approaches. In general we find large effects for volumes below V = (1.8 fm) 4 .

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Section: Numerical Resultsmentioning

confidence: 99%

Volume behavior of quark condensate, pion mass, and decay constant from Dyson-Schwinger equations

2010

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“…The choice of boundary conditions affects the behavior of the pion mass in finite volume [20] as well as the chiral phase transition temperature [21]. For periodic spatial boundary conditions, the presence of a quark zero-momentum mode leads to an enhancement of the chiral condensate.…”

Section: Introductionmentioning

confidence: 99%

“…In many lattice QCD simulations, periodic boundary conditions are chosen in order to minimize finite-volume effects. In a model calculation, we have indeed found that that this choice minimizes finite-volume effects [20].…”

Section: Introductionmentioning

confidence: 99%

Curvature of the QCD phase transition line in a finite volume

Klein¹,

Braun²,

Jena³

et al. 2011

Proceedings of the XXVIII International Symposium on Lattice Field Theory — PoS(Lattice 2010)

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The curvature which characterizes the QCD phase transition at finite temperature and small values of the chemical potential is accessible to lattice simulations. The results for this quantity which have been obtained by several different lattice simulation methods differ due to different numbers of flavors, different pion masses and different sizes of the simulation volume. In order to reconcile these results, it is important to investigate finite-volume effects on the curvature.We investigate the curvature of the chiral phase transition line at finite temperature and chemical potential in a finite volume. We use a phenomenological model for chiral symmetry breaking and apply non-perturbative functional renormalization group methods which account for critical long-range fluctuations at the phase transition.We find an intermediate volume region in which the curvature of the phase transition line is actually reduced relative to its infinite-volume value, provided periodic spatial boundary conditions are chosen for the quark fields. Size and location of this region depend on the value of the pion mass. Such an effect could account for differences in the curvature between lattice simulations in differently sized volumes and from functional methods in the infinite volume limit. We discuss implications of our results for the QCD phase diagram.

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“…This behavior can be indeed observed in our RG analysis once order-parameter fluctuations are taken into account, cf. also previous RG studies of finite-volume effects in QCD low-energy models [43][44][45][46].…”

Section: Beyond Mean-field and The Role Of Fluctuations In A Finimentioning

confidence: 99%

“…For our analysis we employ a functional renormalization group (FRG) approach and apply techniques similar to those used for the analysis of finite-volume effects in QCD low-energy models [43][44][45][46][47]. For our purposes, such an approach is advantageous since it allows us to investigate the "transition" between the finite system and its continuum limit.…”

Section: Introductionmentioning

confidence: 99%

Finite-size and particle-number effects in an ultracold Fermi gas at unitarity

2011

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We investigate an ultracold Fermi gas at unitarity confined in a periodic box V = L 3 using renormalization group (RG) techniques. Within this approach we can quantitatively assess the long range bosonic order parameter fluctuations which dominate finite-size effects. We determine the finite-size and particle-number dependence of universal quantities, such as the Bertsch parameter and the fermion gap. Moreover, we analyze how these universal observables respond to the variation of an external pairing source. Our results indicate that the Bertsch parameter saturates rather quickly to its value in the thermodynamic limit as a function of increasing box size. On the other hand, we observe that the fermion gap shows a significantly stronger dependence on the box size, in particular for small values of the pairing source. Our results may contribute to a better understanding of finitesize and particle-number effects present in Monte-Carlo simulations of ultracold Fermi gases.

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Volume dependence of the pion mass in the quark-meson model

Cited by 66 publications

References 33 publications

Volume behavior of quark condensate, pion mass, and decay constant from Dyson-Schwinger equations

Volume behavior of quark condensate, pion mass, and decay constant from Dyson-Schwinger equations

Curvature of the QCD phase transition line in a finite volume

Finite-size and particle-number effects in an ultracold Fermi gas at unitarity

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