scholarly journals Comparison between the continuum threshold and the Polyakov loop as deconfinement order parameters

2017 ◽  
Vol 95 (3) ◽  
Author(s):  
J. P. Carlomagno ◽  
M. Loewe
Keyword(s):  
Polyakov Loop ◽  
Order Parameters ◽  
Continuum Threshold ◽  
The Continuum

scholarly journals Bridging the two order parameters for the QCD deconfiment phase transition

2018 ◽  
Vol 172 ◽  
pp. 04005 ◽  
Author(s):  
Juan Pablo Carlomagno ◽  
Marcelo Loewe
Keyword(s):  
Chemical Potential ◽  
Sum Rules ◽  
Quark Condensate ◽  
Order Parameters ◽  
Chiral Symmetry Restoration ◽  
Critical Temperatures ◽  
Continuum Threshold ◽  
Baryonic Chemical Potential ◽  
Static Quark ◽  
The Continuum

We study the relation between two order parameters for deconfinement, normally employed in the literature: the continuum threshold s0, in the context of QCD Sum Rules, and the trace of the Polyakov loop ϕ in the framework of a nonlocal SU(2) chiral quark model. We establish a bridge between both order parameters at finite temperature T and baryonic chemical potential μ. In our analysis, we also include the the chiral quark condensate, the order parameter for the chiral symmetry restoration. We found that s0 and ϕ provide us with the same information for the deconfinement transition, both for the zero and finite chemical potential cases. At zero density, the critical temperatures for both quantities coincide exactly. This part of the analysis has been reinforced by the discussion of the corresponding susceptibilities and the static quark entropy behavior. At finite μ both order parameters provide evidence for the appearance of a quarkyonic phase.

scholarly journals Aspects of heavy, dense lattice QCD : series expansion methods, baryon versus isospin density and large Nc

2021 ◽  
Author(s):  
◽  
Jonas Benedict Scheunert
Keyword(s):  
Lattice Qcd ◽  
Series Expansion ◽  
Chemical Potential ◽  
Finite Lattice ◽  
Polyakov Loop ◽  
Cluster Method ◽  
Effective Theory ◽  
Valuable Insight ◽  
Sign Problem ◽  
The Continuum

For finite baryon chemical potential, conventional lattice descriptions of quantum chromodynamics (QCD) have a sign problem which prevents straightforward simulations based on importance sampling. In this thesis we investigate heavy dense QCD by representing lattice QCD with Wilson fermions at finite temperature and density in terms of Polyakov loops. We discuss the derivation of $3$-dimensional effective Polyakov loop theories from lattice QCD based on a combined strong coupling and hopping parameter expansion, which is valid for heavy quarks. The finite density sign problem is milder in these theories and they are also amenable to analytic evaluations. The analytic evaluation of Polyakov loop theories via series expansion techniques is illustrated by using them to evaluate the $\SU{3}$ spin model. We compute the free energy density to $14$th order in the nearest neighbor coupling and find that predictions for the equation of state agree with simulations to $\mathcal{O}(1\%)$ in the phase were the (approximate) $Z(3)$ center symmetry is intact. The critical end point is also determined but with less accuracy and our results agree with numerical results to $\mathcal{O}(10\%)$. While the accuracy for the endpoint is limited for the current length of the series, analytic tools provide valuable insight and are more flexible. Furthermore they can be generalized to Polyakov-loop-theories with $n$-point interactions. We also take a detailed look at the hopping expansion for the derivation of the effective theory. The exponentiation of the action is discussed by using a polymer expansion and we also explain how to obtain logarithmic resummations for all contributions, which will be achieved by employing the finite cluster method know from condensed matter physics. The finite cluster method can also be used to evaluate the effective theory and comparisons of the evaluation of the effective action and a direction evaluation of the partition function are made. We observe that terms in the evaluation of the effective theory correspond to partial contractions in the application of Wick's theorem for the evaluation of Grassmann-valued integrals. Potential problems arising from this fact are explored. Next to next to leading order results from the hopping expansion are used to analyze and compare the onset transition both for baryon and isospin chemical potential. Lattice QCD with an isospin chemical potential does not have a sign problem and can serve as a valuable cross-check. Since we are restricted by the relatively short length of our series, we content ourselves with observing some qualitative phenomenological properties arising in the effective theory which are relevant for the onset transition. Finally, we generalize our results to arbitrary number of colors $N_c$. We investigate the transition from a hadron gas to baryon condensation and find that for any finite lattice spacing the transition becomes stronger when $N_c$ is increased and to be first order in the limit of infinite $N_c$. Beyond the onset, the pressure is shown to scale as $p \sim N_c$ through all available orders in the hopping expansion, which is characteristic for a phase termed quarkyonic matter in the literature. Some care has to be taken when approaching the continuum, as we find that the continuum limit has to be taken before the large $N_c$ limit. Although we currently are unable to take the limits in this order, our results are stable in the controlled range of lattice spacings when the limits are approached in this order.

scholarly journals Equilibrium order parameters of nematic liquid crystals in the Landau-de Gennes theory

2010 ◽  
Vol 21 (2) ◽  
pp. 181-203 ◽  
Author(s):  
APALA MAJUMDAR
Keyword(s):  
Three Dimensional ◽  
Energy Functional ◽  
Order Parameters ◽  
Tensor Order ◽  
Temperature Regimes ◽  
Explicit Bounds ◽  
Scalar Order ◽  
Definition Of ◽  
Gennes Theory ◽  
The Continuum

We study equilibrium liquid crystal configurations in three-dimensional geometries, within the continuum Landau-de Gennes theory. We obtain explicit bounds for the equilibrium scalar order parameters in terms of the temperature and material-dependent constants. We explicitly quantify the temperature regimes where the Landau-de Gennes predictions match and the temperature regimes where the Landau-de Gennes predictions do not match the probabilistic second-moment definition of the Q-tensor order parameter. The regime of agreement may be interpreted as the regime of validity of the Landau-de Gennes theory since the Landau-de Gennes theory predicts large values of the equilibrium scalar order parameters – larger than unity, in the low-temperature regime. We discuss a modified Landau-de Gennes energy functional which yields physically realistic values of the equilibrium scalar order parameters in all temperature regimes.

Possibility of weakly charged nonlinear solitary dust clouds near the continuum threshold of dust population in a quasi-neutral dusty plasma

Pramana ◽  
1998 ◽  
Vol 51 (6) ◽  
pp. 757-771 ◽  
Author(s):  
S. K. Baishya ◽  
Joyanti Chutia ◽  
M. K. Kalita ◽  
G. C. Das ◽  
C. B. Dwivedi
Keyword(s):  
Dusty Plasma ◽  
Continuum Threshold ◽  
Dust Clouds ◽  
The Continuum

Hydrodynamics

2021 ◽  
pp. 49-66
Author(s):  
Robert W. Batterman
Keyword(s):  
Correlation Functions ◽  
Linear Response ◽  
Order Parameters ◽  
Equilibrium States ◽  
Conserved Quantities ◽  
Many Body ◽  
Hydrodynamic Description ◽  
Relative Autonomy ◽  
Many Body Systems ◽  
The Continuum

This chapter begins the argument that the best way to understand the relations of relative autonomy between theories at different scales is through a mesoscale hydrodynamic description of many-body systems. It focuses on the evolution of conserved quantities of those systems in near, but out of equilibrium states. A relatively simple example is presented of a system of spins where the magnetization is the conserved quantity of interest. The chapter introduces the concepts of order parameters, of local quantities, and explains why we should be focused on the gradients of densities that inhabit the mesoscale between the scale of the continuum and that of the atomic. It introduces the importance of correlation functions and linear response.

scholarly journals Charm quark mass determined from a pair of sum rules

2016 ◽  
Vol 31 (37) ◽  
pp. 1630041 ◽  
Author(s):  
Jens Erler ◽  
Pere Masjuan ◽  
Hubert Spiesberger
Keyword(s):  
Quark Mass ◽  
Sum Rules ◽  
Charm Quark ◽  
Vector Current ◽  
Continuum Threshold ◽  
Charm Quark Mass ◽  
Continuum Region ◽  
Continuum Contribution ◽  
The Continuum

In this paper, we present preliminary results of the determination of the charm quark mass [Formula: see text] from QCD sum rules of moments of the vector current correlator calculated in perturbative QCD at [Formula: see text]. Self-consistency between two different sum rules allow to determine the continuum contribution to the moments without requiring experimental input, except for the charm resonances below the continuum threshold. The existing experimental data from the continuum region is used, then, to confront the theoretical determination and reassess the theoretic uncertainty.

scholarly journals PION FORM FACTOR IN QCD SUM RULES WITH NONLOCAL CONDENSATES AND IN THE LOCAL-DUALITY APPROACH

2009 ◽  
Vol 24 (35n37) ◽  
pp. 2848-2857 ◽  
Author(s):  
A. P. BAKULEV ◽  
A. V. PIMIKOV ◽  
N. G. STEFANIS
Keyword(s):  
Form Factor ◽  
Sum Rules ◽  
Pion Form Factor ◽  
Analytic Perturbation Theory ◽  
Continuum Threshold ◽  
Sum Rule ◽  
Local Duality ◽  
Rule Approach ◽  
Duality Approach ◽  
The Continuum

We discuss the QCD sum-rule approach for the spacelike electromagnetic pion form factor in the O(αs) approximation. We show that the nonlocality of the condensates is a key point to include nonperturbative contributions to the pion form factor. We compare our results with the Local-Duality predictions and show that the continuum threshold s0(Q2) parameter is highly underestimated in the Local-Duality approach at Q2 ≳ 2 GeV 2. Using our fit for this parameter, [Formula: see text] and applying the fractional analytic perturbation theory, we estimate with an accuracy of the order of 1% the [Formula: see text] contribution to the pion's form factor.

scholarly journals Evidence for the unbinding of the 𝜙4 kink’s shape mode

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Jarah Evslin
Keyword(s):  
Quantum Correction ◽  
The Other ◽  
Meson Mass ◽  
Continuum Threshold ◽  
Kink Solution ◽  
Other Hand ◽  
The Continuum

Abstract The 𝜙4 double-well theory admits a kink solution, whose rich phenomenology is strongly affected by the existence of a single bound excitation called the shape mode. We find that the leading quantum correction to the energy needed to excite the shape mode is −0.115567λ/M in terms of the coupling λ/4 and the meson mass M evaluated at the minimum of the potential. On the other hand, the correction to the continuum threshold is −0.433λ/M. A naive extrapolation to finite coupling then suggests that the shape mode melts into the continuum at the modest coupling of λ/4 ∼ 0.106M2, where the ℤ2 symmetry is still broken.

Sign in / Sign up

Export Citation Format

Share Document