Finite Temperature Chiral Phase Transition Research Articles

Critical exponents of finite temperature chiral phase transition in soft-wall AdS/QCD models

Criticality of chiral phase transition at finite temperature is investigated in a soft-wall AdS/QCD model, with two, three degenerate flavors (Nf = 2, 3) and two light plus one heavier flavor (Nf = 2 + 1). It is shown that in quark mass plane (mu/d − ms) chiral phase transition is second order at a certain critical line, by which the whole plane is divided into first order and crossover regions. The critical exponents β and δ, describing critical behavior of chiral condensate along temperature axis and light quark mass axis, are extracted both numerically and analytically. The model gives the critical exponents of the values beta =frac{1}{2},delta =3 and beta =frac{1}{3},delta =3 for Nf = 2 and Nf = 3 respectively. For Nf = 2 + 1, in small strange quark mass (ms) region, the phase transitions for strange quark and u/d quarks are strongly coupled, and the critical exponents are beta =frac{1}{3},delta =3 ; when ms is larger than ms,t = 0.290 GeV, the dynamics of light flavors (u, d) and strange quarks decoupled and the critical exponents for ūu and overline{d}d becomes beta =frac{1}{2},delta =3 , exactly the same as Nf = 2 result and the mean field result of 3D Ising model; between the two segments, there is a tri-critical point at ms,t = 0.290 GeV, at which beta =frac{1}{4},delta =5 . In some sense, the current results is still at mean field level, and we also showed the possibility to go beyond mean field approximation by including the higher power of scalar potential and the temperature dependence of dilaton field, which might be reasonable in a full back-reaction model. The current study might also provide reasonable constraints on constructing a realistic holographic QCD model, which could describe both chiral dynamics and glue-dynamics correctly.

Thermodynamic Lattice Study for Preconformal Dynamics in Strongly Flavored Gauge Theory

By using the lattice Monte-Carlo simulation, we investigate the finite temperature chiral phase transition in color SU(3) gauge theories with various species of fundamental fermions, and discuss the signals of the (pre-)conformality at large Nf (number of flavors) via their comparisons. With increasing Nf, we confirm stronger fermion screening which results from a larger fermion multiplicity. We investigate a finite T step-scaling which is attributed to the uniqueness of the critical temperature (Tc) at each Nf, then the vanishing step-scaling signals the emergence of the conformality around N*f ∼ 10−12. Further, motivated by the recent functional renormalization group analyses, we examine the Nf dependence of Tc, whose vanishing behavior indicates that the conformal phase sets in around N*f ∼ 9 − 10.

Anomaly and a QCD-like phase diagram with massive bosonic baryons

We study a strongly coupled $Z_2$ lattice gauge theory with two flavors of quarks, invariant under an exact $\mathrm{SU}(2)\times \mathrm{SU}(2) \times \mathrm{U}_A(1) \times \mathrm{U}_B(1)$ symmetry which is the same as QCD with two flavors of quarks without an anomaly. The model also contains a coupling that can be used to break the $\mathrm{U}_A(1)$ symmetry and thus mimic the QCD anomaly. At low temperatures $T$ and small baryon chemical potential $\mu_B$ the model contains massless pions and massive bosonic baryons similar to QCD with an even number of colors. In this work we study the $T-\mu_B$ phase diagram of the model and show that it contains three phases : (1) A chirally broken phase at low $T$ and $\mu_B$, (2) a chirally symmetric baryon superfluid phase at low $T$ and high $\mu_B$, and (3) a symmetric phase at high $T$. We find that the nature of the finite temperature chiral phase transition and in particular the location of the tricritical point that seperates the first order line from the second order line is affected significantly by the anomaly.

Chiral and critical behavior in strong coupling QCD

We use a cluster algorithm to study the critical behavior of strongly coupled lattice QCD in the chiral limit. We show that the finite temperature chiral phase transition belongs to the O(2) universality class as expected. When we compute the finite size effects of the chiral susceptibility in the low temperature phase close to the transition, we find clear evidence for chiral singularities predicted by chiral perturbation theory (ChPT). On the other hand it is difficult to reconcile the quark mass dependence of various quantities near the chiral limit with ChPT.

Meron-cluster algorithms and chiral-symmetry breaking in a (2+1)D staggered fermion model

The recently developed Meron-Cluster algorithm completely solves the exponentially difficult sign problem for a number of models previously inaccessible to numerical simulation. We use this algorithm in a high-precision study of a model of N=1 flavor of staggered fermions in (2+1)-dimensions with a four-fermion interaction. This model cannot be explored using standard algorithms. We find that the Z(2) chiral symmetry of this model is spontaneously broken at low temperatures and that the finite-temperature chiral phase transition is in the universality class of the 2-d Ising model, as expected.

Meron-cluster simulation of a chiral phase transition with staggered fermions

We examine a (3+1)-dimensional model of staggered lattice fermions with a four-fermion interaction and Z(2) chiral symmetry using the Hamiltonian formulation. This model cannot be simulated with standard fermion algorithms because those suffer from a very severe sign problem. We use a new fermion simulation technique — the meron-cluster algorithm — which solves the sign problem and leads to high-precision numerical data. We investigate the finite temperature chiral phase transition and verify that it is in the universality class of the 3-d Ising model using finite-size scaling.

The three flavour chiral phase transition with an improved quark and gluon action in lattice QCD

The finite-temperature chiral phase transition is investigated for three flavours of staggered quarks on a lattice of temporal extent N τ = 4. In the simulation we use an improved fermion action which reduces rotational symmetry breaking of the quark propagator (p4-action), include fat-links to improve the flavour symmetry and use the tree level improved (1,2) gluon action. We study the nature of the phase transition for quark masses of ma = 0.025, ma = 0.05 and ma = 0.1 on lattices with spatial sizes of 8 3 and 16 3.

Scaling study of the two-flavor chiral phase transition with the Kogut-Susskind quark action in lattice QCD

We report on a study of the two-flavor finite-temperature chiral phase transition employing the Kogut-Susskind quark action and the plaquette gluon action in lattice QCD for a lattice with ${N}_{t}=4$ temporal size. Hybrid $R$ simulations of ${10}^{4}$ trajectories are made at quark masses of ${m}_{q}=0.075,0.0375,0.02,0.01$ in lattice units for the spatial sizes ${8}^{3}{,12}^{3}$, and ${16}^{3}$. The spatial size dependence of various susceptibilities confirm the previous conclusion of the absence of a phase transition down to ${m}_{q}=0.02$. At ${m}_{q}=0.01$ an increase of susceptibilities is observed up to the largest volume ${16}^{3}$ explored in the present work. We argue, however, that this increase is likely to be due to an artifact of too small a lattice size and it cannot be taken to be the evidence for a first-order transition. Analysis of critical exponents estimated from the quark mass dependence of susceptibilities shows that they satisfy hyperscaling consistent with a second-order transition located at ${m}_{q}=0$. The exponents obtained from larger lattice, however, deviate significantly from both those of O(2), which is the exact symmetry group of the Kogut-Susskind action at finite lattice spacing, and those of O(4) expected from an effective $\ensuremath{\sigma}$ model analysis in the continuum limit.

Two-flavor chiral phase transition in lattice QCD with the Kogut-Susskind quark action

A summary is presented of a scaling study of the finite-temperature chiral phase transition of two-flavor QCD with the Kogut-Susskind quark action based on simulations on L 3 × 4 ( L = 8, 12, and 16) lattices at the quark mass of m q = 0.075, 0.0375, 0.02 and 0.01. We find a phase transition to be absent for m q ≥ 0.02, and also quite likely at m q = 0.01. The quark mass dependence of susceptibilities is consistent with a second-order transition at m q = 0. The exponents, however, deviate from the O(2) and O(4) values theoretically expected.

Scaling analysis of chiral phase transition for two flavors of kogut-Susskind quarks

Report is made of a systematic scaling study of the finite-temperature chiral phase transition of two-flavor QCD with the Kogut-Susskind quark action based on simulations on $L^3\times4$ ($L$=8, 12 and 16) lattices at the quark mass of $m_q=0.075, 0.0375, 0.02$ and 0.01. Our finite-size data show that a phase transition is absent for $m_q\geq 0.02$, and quite likely also at $m_q=0.01$. The scaling behavior of susceptibilities as a function of $m_q$ is consistent with a second-order transition at $m_q=0$. However, the exponents deviate from the O(2) or O(4) values theoretically expected.

Some properties of the finite temperature chiral phase transition.

We study the phase transition of the (3+1)-dimensional Yukawa model at finite temperature. We calculate the critical exponents in the 1/[ital N] expansion and clarify certain subtleties involved in such a calculation. In the leading order we do not find the presence of any of the metastable states which were claimed in the literature. To this order, the exponents are the mean field, but corrections shift them to the usual nontrivial values. Dimensional reduction of this model is studied with special attention paid to the discrete symmetries of the Lagrangian before and after reduction. In the reduced [ital d]=3 theory there are two possible types of mass terms, one of which is allowed by chiral symmetry. It is the different discrete symmetries of these two mass terms which force the finite temperature 3 + 1 Yukawa Lagrangian to reduce to the usual scalar universality class (characterized by a conformally invariant [sigma] model) rather than the chiral universality class (characterized by [ital d]=3 conformally invariant NJL-type model).

Fluctuation induced first order phase transitions

We study a U ( N) × U ( N) symmetric scalar field model in four and three dimensions. First, using our data in four dimensions in the weak coupling region, we demonstrate explicitly that the observed first order phase transition is induced by quantum fluctuations. Next, based on the renormalization group and our new simulation results in three dimensions we argue that even if the U A (1) symmetry is restored below the critical temperature the QCD finite temperature chiral phase transition for two flavor could be extremely weak first order.

Coexistence of broken and restored chiral symmetry in the baryon sector

The solitonic baryon model with a quantized cut-off, proposed recently by Balakrishna et al. is modified to describe a bubble of the chiral symmetric phase immerged into the broken phase. The results of the quantum mechanical treatment of the bubble radius are compared to some characteristic features of the baryon spectra. A possible relevance of the model to the baryon density contrast emerging at the finite temperature chiral phase transition in the Universe is also discussed.

On the order of the phase transition in three-dimensionalSU( N)⊗SU( N) and U( N)⊗U( N) Heisenberg models and finite temperature QCD

The finite temperature QCD chiral phase transition for massless SU(2), SU(3), U(2), and U(3) flavor groups is studied using the chiral Heisenberg model. A variety of numerical techniques, including metastability analysis, reduced cumulant of the energy, and finite size scaling were employed to determine the order of the finite temperature chiral phase transition for these flavor symmetries. The SU(2) Heisenberg model had a second order transition while the SU(3), U(2) and U(3) models were first order transitions.

APPLICATION OF MONOMER-DIMER ALGORITHMS IN STRONG COUPLING QCD

We study the finite temperature chiral phase transition of SU(3) lattice QCD in the strong coupling limit using the monomer dimer polymer MDP representation of the partition function. By Monte Carlo simulation we measured the chiral condensate and the susceptibility as a function of temperature for various values of the quark mass. The effect of a global symmetry of the lattice action is discussed in terms of critical exponents.

Finite-size study of the finite-temperature chiral phase transition in QCD with light quarks

Finite-size tests were carried out for the finite-temperature chiral phase transition in QCD on a lattice with 4 times slices usign the Kogut-Susskind quark action at the quark mass of 0.025 ( N f = 4 and 2) and 0.0125 ( N f = 2) in lattice units. For N f = 4, all the evidence supports a supports a first-order transition. for N f = 2, however, the data up to a 12 3 spatial lattice do not yield finite-size signatures for a first-order transition of these quark masses.

Further study of the finite-temperature chiral phase transition of two-flavor lattice QCD at a small quark mass

A previous finite-size study for the chiral phase transition of two-flavor QCD is extended to a smaller quark mass of ${m}_{q}=0.0125$ in lattice units. The characteristics of the system for lattice sizes (${6}^{3}$ - ${12}^{3}$) \ifmmode\times\else\texttimes\fi{} 4 are found to be quite similar to those for ${m}_{q}=0.0025$. The increase of susceptibilities over this range of the spatial size is still too mild to discriminate among the order of the transition also at this small quark mass.

Finite-size test for the finite-temperature chiral phase transition in lattice QCD.

A finite-size test was carried out for the finite-temperature chiral phase transition in QCD for flavor number ${\mathit{N}}_{\mathit{f}}$=4 and 2 on a lattice with four time slices using the Kogut-Susskind quark action at quark mass of 0.025 in lattice units. All the evidence supports a first-order transition for ${\mathit{N}}_{\mathit{f}}$=4. For ${\mathit{N}}_{\mathit{f}}$=2, however, the data on spatial lattice up to ${12}^{3}$ fail to yield convincing finite-size signatures for a first-order transition at this quark mass.

Hybrid simulations with dynamical quarks: Spectra, screening and thermodynamics

We summarize simulations made by the Argonne/University of Illinois group using the Hybrid algorithm to include dynamical staggered fermions. Recent work on the mass spectrum and screening effects due to the inclusion of four light flavours of dynamical quarks is presented. We also present a brief overview of what we have learned about the finite temperature chiral phase transition.

On the order of the finite temperature chiral phase transition in QCD

A differential renormalisation group equation is derived for the effective potential of the chiral order parameter of a theory with N f light flavors. Its solution for N f = 3 provides further support to the first-order nature of the finite temperature restoration of chiral symmetry in QCD.