Volume and quark mass dependence of the chiral phase transition

Braun, Jens; Klein, Bertram; Pirner, H. J.; Rezaeian, Amir H.

doi:10.1103/physrevd.73.074010

Cited by 78 publications

(115 citation statements)

References 60 publications

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“…Nevertheless, our findings for the behavior of the critical temperature as a function of both the pion mass and the isospin chemical potential are in remarkably good agreement with lattice data. It is crucial to note that several detailed studies of chiral models failed to describe T c (m π ) [5,6,7], while Polyakov-loop models, whose predictions can be fitted to the lattice points for T c (m π ) [5], cannot at the present form address isospin effects. In this approach, we can also investigate in a straightforward manner the effects of quark-mass asymmetry and nonzero baryon chemical potential, physical cases in which the Sign Problem develops, constraining systematic lattice studies.…”

mentioning

confidence: 99%

Quark mass and isospin dependence of the deconfining critical temperature

2009

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We describe the deconfining critical temperature dependence on the pion mass and on the isospin chemical potential in remarkably good agreement with lattice data. Our framework incorporates explicit dependence on quark masses, isospin and baryonic chemical potentials for the case of two flavors through ingredients from well-known high-and low-energy theories. In the low-energy sector, the system is described by a minimal chiral perturbation theory effective action, corresponding to a hot gas of pion quasiparticles and heavy nucleons. For the high-temperature sector we adopt a simple extension of the fuzzy bag model. We also briefly discuss the effects of mass asymmetry and baryon chemical potential.Introduction. The phase diagram of quark matter has been the object of intense investigation during the last years, and yet several open questions within the thermodynamics of strong interactions still remain unsolved [1,2]. In this quest, Lattice QCD represents the main non-perturbative approach within the full theory [3], always complemented by effective models [4].In this article we investigate the effects of finite quark masses and isospin number on the equation of state of hot and dense strongly interacting matter and on the deconfining phase transition within a framework inspired by chiral perturbation theory (χPT) and lattice results for the pressure and the trace anomaly. The setting we propose is simple and completely fixed by vacuum QCD properties (measured or simulated on the lattice) and lattice simulations of finite temperature QCD. More explicitly, there is no fitting of mass or isospin chemical potential dependence at all. Nevertheless, our findings for the behavior of the critical temperature as a function of both the pion mass and the isospin chemical potential are in remarkably good agreement with lattice data. It is crucial to note that several detailed studies of chiral models failed to describe T c (m π ) [5,6,7], while Polyakov-loop models, whose predictions can be fitted to the lattice points for T c (m π ) [5], cannot at the present form address isospin effects. In this approach, we can also investigate in a straightforward manner the effects of quark-mass asymmetry and nonzero baryon chemical potential, physical cases in which the Sign Problem develops, constraining systematic lattice studies. The predictions within our framework for these regimes which are not yet fully probed by lattice QCD are left for a longer publication (for preliminary results, see [8]). Throughout the present paper, the baryon chemical potential is fixed to zero. It is not our aim in this short paper to provide a complete description of the full richness of the QCD phase diagram. Still, we present a description of the dependence of the critical deconfining temperature on the quark-average mass and on the isospin chemical potential simultaneously.Small quark masses and a nonzero baryon chemical po-

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confidence: 99%

Quark mass and isospin dependence of the deconfining critical temperature

2009

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“…By solving the flow equation for the effective action in the above ansatz, we obtain in the limit k → 0 the full effective action, including the effects of longrange fluctuations. The method can be adapted to a finite Euclidean space-time volume L 3 × 1/T [20,21,25,26] by considering sums over discrete momentum modes instead of the continuous momentum integrations of the infinite-volume case. We solve the RG flow equation numerically by using an expansion of the local potential around its minimum; any additional momentum dependence of the couplings is neglected.…”

Section: Model and Methodsmentioning

confidence: 99%

“…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%

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 and quark mass dependence of the chiral phase transition

Cited by 78 publications

References 60 publications

Quark mass and isospin dependence of the deconfining critical temperature

Quark mass and isospin dependence of the deconfining critical temperature

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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