APPLICATION OF THE RENORMALIZATION GROUP TO A SECOND-ORDER QCD PHASE TRANSITION

1992 ◽  
Vol 07 (16) ◽  
pp. 3911-3925 ◽  
Author(s):  
FRANK WILCZEK
Keyword(s):  
Phase Transition ◽  
Renormalization Group ◽  
Strange Quark ◽  
Tricritical Point ◽  
Universality Class ◽  
Second Order ◽  
Chiral Phase ◽  
Quark Masses ◽  
Potential Applications ◽  
Second Order Transition

An earlier suggestion that the chiral phase transition in QCD for two flavors of massless quarks might be a second-order transition has gained credibility as a result of recent numerical simulations. One can test this hypothesis, and draw very specific quantitative consequences from it, using universality and renormalization group ideas. This hypothetical second order phase transition is in the universality class of a four component isotropic Heisenberg antiferromagnet—a model which has been investigated intensely by condensed matter physicists. Existing calculations can be adapted to yield predictions for critical exponents governing the QCD transition. The perturbation due to small equal quark masses maps onto an external staggered magnetic field; that due to unequal quark masses is effective only in second order and generates a quadratic anisotropy. Several other potential applications of the renormalization group to related questions are suggested, including a model of the tricritical point which arises with finite strange quark mass, and a model for the dynamic critical behavior.

scholarly journals Detecting scale anomaly in chiral phase transition of QCD: new critical endpoint pinned down

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Mamiya Kawaguchi ◽  
Shinya Matsuzaki ◽  
Akio Tomiya
Keyword(s):  
Magnetic Field ◽  
Phase Transition ◽  
Weak Magnetic Field ◽  
Strange Quark ◽  
Strong Field ◽  
Dense Matter ◽  
Second Order ◽  
Chiral Phase ◽  
Chiral Phase Transition ◽  
Matter System

Abstract Violation of scale symmetry, scale anomaly, being a radical concept in quantum field theory, is of importance to comprehend the vacuum structure of QCD, and should potentially contribute to the chiral phase transition in thermal QCD, as well as the chiral and U(1) axial symmetry. Though it should be essential, direct evidence of scale anomalies has never been observed in the chiral phase transition. We propose a methodology to detect a scale anomaly in the chiral phase transition, which is an electromagnetically induced scale anomaly: apply a weak magnetic field background onto two-flavor massless QCD with an extremely heavy strange quark, first observe the chiral crossover; second, adjusting the strange quark mass to be smaller and smaller, observe the second-order chiral phase transition, and then the first-order one in the massless-three flavor limit. Thus, the second-order chiral phase transition, observed as the evidence of the quantum scale anomaly, is a new critical endpoint. It turns out that this electromagnetic scale anomaly gets most operative in the weak magnetic field regime, rather than a strong field region. We also briefly address accessibility of lattice QCD, a prospected application to dense matter system, and implications to astrophysical observations, such as gravitational wave productions provided from thermomagnetic QCD-like theories.

scholarly journals BARYOGENESIS VIA DENSITY FLUCTUATIONS WITH A SECOND ORDER ELECTROWEAK PHASE TRANSITION

2003 ◽  
Vol 18 (26) ◽  
pp. 4851-4868 ◽  
Author(s):  
BISWANATH LAYEK ◽  
SOMA SANYAL ◽  
AJIT M. SRIVASTAVA
Keyword(s):  
Phase Transition ◽  
Baryon Asymmetry ◽  
Density Fluctuations ◽  
Second Order ◽  
Baryon Production ◽  
Electroweak Phase Transition ◽  
Expansion Of The Universe ◽  
Second Order Transition ◽  
Background Temperature ◽  
The Universe

We consider the presence of cosmic string induced density fluctuations in the universe at temperatures below the electroweak phase transition temperature. Resulting temperature fluctuations can restore the electroweak symmetry locally, depending on the amplitude of fluctuations and the background temperature. The symmetry will be spontaneously broken again in a given fluctuation region as the temperature drops there (for fluctuations with length scales smaller than the horizon), resulting in the production of baryon asymmetry. The time scale of the transition will be governed by the wavelength of fluctuation and, hence, can be much smaller than the Hubble time. This leads to strong enhancement in the production of baryon asymmetry for a second order electroweak phase transition as compared to the case when transition happens due to the cooling of the universe via expansion. For a two-Higgs extension of the Standard Model (with appropriate CP violation), we show that one can get the required baryon to entropy ratio if fluctuations propagate without getting significantly damped. If fluctuations are damped rapidly, then a volume factor suppresses the baryon production. Still, the short scale of the fluctuation leads to enhancement of the baryon to entropy ratio by at least 3–4 orders of magnitude compared to the conventional case of second order transition where the cooling happens due to expansion of the universe.

The spontaneous polarization as evidence for lithium disordering in LiNbO3

1990 ◽  
Vol 5 (9) ◽  
pp. 1933-1939 ◽  
Author(s):  
Dunbar P. Birnie
Keyword(s):  
Phase Transition ◽  
Spontaneous Polarization ◽  
Paraelectric Phase ◽  
Second Order ◽  
Polarization Data ◽  
Paraelectric Phase Transition ◽  
Microscopic Mechanism ◽  
Second Order Transition ◽  
Displacement Model ◽  
Insight Into

The ferroelectric to paraelectric phase transition in lithium niobate is examined. The present study focuses on the microscopic mechanism for this phase transition. Literature reports that give insight into this mechanism are reviewed. Two alternate mechanisms for this second order transition have been discussed previously. The phase transition has been proposed to occur by either (a) cooperative displacement of Li ions or (b) statistical disordering of Li between two octahedral sites in the structure. The present study develops a general Landau expression for the second order phase transition. The spontaneous polarization of the lattice is used as an indicator of the extent of transformation. Then both displacement and disordering models are explored. These are compared with the observed spontaneous polarization data. It is concluded that the spontaneous polarization data are indicative of a Li disordering model, rather than a Li displacement model.

scholarly journals On the order of the QCD chiral phase transition for different numbers of quark flavours

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Francesca Cuteri ◽  
Owe Philipsen ◽  
Alessandro Sciarra
Keyword(s):  
Phase Transition ◽  
Parameter Space ◽  
Chiral Limit ◽  
Lattice Parameter ◽  
Second Order ◽  
Critical Surface ◽  
Chiral Phase ◽  
Chiral Phase Transition ◽  
First Order ◽  
The Continuum

Abstract The nature of the QCD chiral phase transition in the limit of vanishing quark masses has remained elusive for a long time, since it cannot be simulated directly on the lattice and is strongly cutoff-dependent. We report on a comprehensive ongoing study using unimproved staggered fermions with Nf ∈ [2, 8] mass-degenerate flavours on Nτ ∈ {4, 6, 8} lattices, in which we locate the chiral critical surface separating regions with first-order transitions from crossover regions in the bare parameter space of the lattice theory. Employing the fact that it terminates in a tricritical line, this surface can be extrapolated to the chiral limit using tricritical scaling with known exponents. Knowing the order of the transitions in the lattice parameter space, conclusions for approaching the continuum chiral limit in the proper order can be drawn. While a narrow first-order region cannot be ruled out, we find initial evidence consistent with a second-order chiral transition in all massless theories with Nf ≤ 6, and possibly up to the onset of the conformal window at 9 ≲ $$ {N}_{\mathrm{f}}^{\ast } $$ N f ∗ ≲ 12. A reanalysis of already published $$ \mathcal{O} $$ O (a)-improved Nf = 3 Wilson data on Nτ ∈ [4, 12] is also consistent with tricritical scaling, and the associated change from first to second-order on the way to the continuum chiral limit. We discuss a modified Columbia plot and a phase diagram for many-flavour QCD that reflect these possible features.

scholarly journals The Chiral Phase Transition of Hot QCD from the Exact Renormalization Group

2006 ◽  
Vol 115 (1) ◽  
pp. 165-188 ◽  
Author(s):  
D. Shimizube ◽  
J.-I. Sumi
Keyword(s):  
Phase Transition ◽  
Renormalization Group ◽  
Chiral Phase ◽  
Chiral Phase Transition ◽  
Exact Renormalization Group

CONFORMALITY LOST

2010 ◽  
Vol 25 (02n03) ◽  
pp. 422-432 ◽  
Author(s):  
D. B. KAPLAN ◽  
J.-W. LEE ◽  
D. T. SON ◽  
M. A. STEPHANOV
Keyword(s):  
Phase Transition ◽  
Fixed Point ◽  
Inverse Correlation ◽  
Universality Class ◽  
Zero Temperature ◽  
Chiral Phase ◽  
Quantum Theories ◽  
Mass Gap ◽  
Zero Coupling ◽  
Bkt Phase Transition

We consider zero-temperature transitions from conformal to non-conformal phases in quantum theories. We argue that there are three generic mechanisms for the loss of conformality: (i) fixed point goes to zero coupling, (ii) fixed point runs off to infinite coupling, or (iii) an IR fixed point annihilates with a UV fixed point and they both disappear into the complex plane. We give examples of the last case and show that the critical behavior of the mass gap is similar to that of the inverse correlation length in the finite temperature Berezinskii-Kosterlitz-Thouless (BKT) phase transition, ξ ~ exp (c/|T-Tc|1/2). We speculate that the chiral phase transition in QCD at large number of fermion flavors belongs to this universality class, and attempt to identify the UV fixed point that annihilates with the Banks-Zaks fixed point at the lower end of the conformal window.

scholarly journals FIRST AND SECOND ORDER PHASE TRANSITIONS IN MAXWELL–CHERN–SIMONS THEORY COUPLED TO FERMIONS

1996 ◽  
Vol 11 (04) ◽  
pp. 777-822 ◽  
Author(s):  
KEI-ICHI KONDO
Keyword(s):  
Phase Transition ◽  
Chiral Symmetry ◽  
Dyson Equation ◽  
Second Order ◽  
Spontaneous Breaking ◽  
Simons Theory ◽  
Chiral Phase ◽  
Chiral Phase Transition ◽  
Chern Simons ◽  
Chern Simons Theory

In the Maxwell–Chern–Simons theory coupled to Nf flavors of four-component fermions (or an even number of two-component fermions), we construct the gauge-covariant effective potential written in terms of two order parameters which are able to probe the breakdown of chiral symmetry and parity. In the absence of the bare Chern–Simons term, we show that the chiral symmetry is spontaneously broken for fermion flavors Nf below a certain finite critical number [Formula: see text] while the parity is not broken spontaneously. This chiral phase transition is of the second order. In the presence of the bare Chern–Simons term, on the other hand, the chiral phase transition associated with the spontaneous breaking of chiral symmetry is shown to continue to exist, although the parity is explicitly broken. However, it is shown that the existence of the bare Chern–Simons term changes the order of the chiral transition into the first order, no matter how small the bare Chern–Simons coefficient may be. This gauge-invariant result is consistent with that recently obtained through the Schwinger–Dyson equation in the nonlocal gauge.

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