arXiv subjects

J. B. Kogut

Publications and source records attributed to J. B. Kogut.

At least 55 records · Page 3Linked to original sources

arXiv2003

Lattice QCD at finite isospin density and/or temperature

We simulate two-flavour lattice QCD with at a finite chemical potential $μ_I$ for isospin, and finite temperature. At small $μ_I$, we determine the position of the crossover from hadronic matter to a quark-gluon plasma as a function of $μ_I$. At larger $μ_I$ we observe the phase transition from the superfluid pion-condensed phase to a quark-gluon plasma, noting its change from second order to first order as $μ_I$ is increased. We also simulate two-flavour lattice QCD at zero quark mass, using an action which includes an additional 4-fermion interaction, at temperatures close to the chiral transition on $N_t=8$ lattices.

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arXiv2003

Exact constraints on the QCD Phase Diagram

We derive exact constraints relating QCD at nonzero baryon chemical potential and temperature to QCD at nonzero isospin chemical potential and temperature, a theory which can be simulated by conventional methods. These results challenge the consistency of dynamical models of superconductivity and superfluidity in QCD.

hep-ph↗

arXiv2003

The pseudo-Goldstone spectrum of 2-colour QCD at finite density

We examine the spectrum of 2-colour lattice QCD with 4 continuum flavours at a finite chemical potential ($μ$) for quark-number, on a $12^3 \times 24$ lattice. First we present evidence that the system undergoes a transition to a state with a diquark condensate, which spontaneously breaks quark number at $μ=m_π/2$, and that this transition is mean field in nature. We then examine the 3 states that would be Goldstone bosons at $μ=0$ for zero Dirac and Majorana quark masses. The predictions of chiral effective Lagrangians give a good description of the behaviour of these masses for $μ< m_π/2$. Except for the heaviest of these states, these predictions diverge from our measurements, once $μ$ is significantly greater than $m_π/2$. However, the qualitative behaviour of these masses, indicates that the physics is very similar to that predicted by these effective Lagrangians, and there is some indication that at least part of these discrepancies is due to saturation, a lattice artifact.

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arXiv2003

Isospin Chemical Potential and the QCD Phase Diagram at Nonzero Temperature and Baryon Chemical Potential

We use the Nambu--Jona-Lasinio model to study the effects of the isospin chemical potential on the QCD phase diagram at nonzero temperature and baryon chemical potential. We find that the phase diagram is qualitatively altered by a small isospin chemical potential. There are two first order phase transitions that end in two critical endpoints, and there are two crossovers at low baryon chemical potential. These results have important consequences for systems where both baryon and isospin chemical potentials are nonzero, such as heavy ion collision experiments. Our results are in complete agreement with those recently obtained in a Random Matrix Model.

hep-ph↗

arXiv2003

The N_t=4 finite temperature phase transition for lattice QCD with a weak chiral 4-fermion interaction

We study the finite temperature phase transition of lattice QCD with an irrelevant chiral 4-fermion interaction and two massless quark flavours, on $8^3 \times 4$ and $12^2 \times 24 \times 4$ lattices. The strength of the 4-fermion interaction was reduced to half the minimum value used in previous simulations, to study how the nature of this phase transition depends on this additional interaction. We find that the transition remains first order as the 4-fermion coupling is reduced. Extending our earlier studies indicates that for sufficiently large 4-fermion coupling, the transition is probably second order.

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arXiv2002

The chiral limit of non-compact QED(3)

Non-compact QED(3) with four-component fermion flavor content larger than or equal to two is studied numerically near the chiral limit to understand its chiral symmetry breaking features. We monitor discretization and finite size effects on the chiral condensate by simulating the model at different values of the gauge coupling on lattices ranging in size from 10^3 to 50^3. Our upper bound for the dimensionless condensate beta^2 in the N_f=2 case is 5x10^{-5}.

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arXiv2002

Lattice QCD at finite isospin chemical potential and temperature

We simulate lattice QCD at a finite chemical potential $μ_I$ for isospin ($I_3$) at zero and finite temperatures. At some $μ_I=μ_c$ QCD has a second order transition with mean-field critical exponents to a state where ($I_3$) is broken spontaneously by a charged pion condensate. Heating the system with $μ_I > μ_c$ we find there is some temperature at which this condensate evaporates. This transition appears to be second order and mean-field at lower $μ_I$ values, and first order for $μ_I$ sufficiently large. We are determining the dependence of the finite temperature crossover $T_c$ on $μ_I$ for $μ_I < μ_c$. This is expected to be identical to $T_c$'s dependence on quark-number chemical potential $μ_q$ for small $μ_q$.

hep-lat↗

arXiv2002

Non-compact QED_3 with N_f >=2

Non-compact three-dimensional QED is studied by computer simulations to understand its chiral symmetry breaking features for N_f>=2, on lattice volumes up to 50^3 and bare masses as low as ma=0.0000625. We compute the chiral condensate, scalar and pseudoscalar susceptibilities, and the masses of scalar and pseudoscalar mesons. Finite volume effects and discretisation artifacts are carefully monitored. Our results reveal no decisive signal for chiral symmetry breaking for any N_f>=2. For N_f=2 the dimensionless condensate can be bounded by beta^2 <= 5x10^-5. We also present an exploratory study of the fractionally-charged Polyakov line.

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arXiv2002

Application of the Maximum Entropy Method to the (2+1)d Four-Fermion Model

We investigate spectral functions extracted using the Maximum Entropy Method from correlators measured in lattice simulations of the (2+1)-dimensional four-fermion model. This model is particularly interesting because it has both a chirally broken phase with a rich spectrum of mesonic bound states and a symmetric phase where there are only resonances. In the broken phase we study the elementary fermion, pion, sigma and massive pseudoscalar meson; our results confirm the Goldstone nature of the pi and permit an estimate of the meson binding energy. We have, however, seen no signal of sigma -> pi pi decay as the chiral limit is approached. In the symmetric phase we observe a resonance of non-zero width in qualitative agreement with analytic expectations; in addition the ultra-violet behaviour of the spectral functions is consistent with the large non-perturbative anomalous dimension for fermion composite operators expected in this model.

hep-lat↗

arXiv2002

Lattice QCD at finite isospin density at zero and finite temperature

We simulate lattice QCD with dynamical $u$ and $d$ quarks at finite chemical potential, $μ_I$, for the third component of isospin ($I_3$), at both zero and at finite temperature. At zero temperature there is some $μ_I$, $μ_c$ say, above which $I_3$ and parity are spontaneously broken by a charged pion condensate. This is in qualitative agreement with the prediction of effective (chiral) Lagrangians which also predict $μ_c=m_π$. This transition appears to be second order, with scaling properties consistent with the mean-field predictions of such effective Lagrangian models. We have also studied the restoration of $I_3$ symmetry at high temperature for $μ_I > μ_c$. For $μ_I$ sufficiently large, this finite temperature phase transition appears to be first order. As $μ_I$ is decreased it becomes second order connecting continuously with the zero temperature transition.

hep-lat↗

arXiv2002

Quenched lattice QCD at finite isospin density and related theories

We study quenched QCD at finite chemical potential, $μ_I$, for the third component of isospin and quenched two-colour QCD at finite chemical potential, $μ$, for quark number. In contrast to the quenched approximation to QCD at finite quark-number chemical potential, the quenched approximations to these theories behave similarly to the full theories. The reason is that these theories have real positive fermion determinants. In both of these theories there is some critical chemical potential above which the charge coupled to the chemical potential is spontaneously broken. In each case, the transition appears to be second order. We study the scaling properties near the critical point using scaling functions suggested by effective (chiral) Lagrangians and find evidence for scaling with mean-field critical exponents in each case. The subtleties associated with observing the critical scaling of these theories are discussed.

hep-lat↗

arXiv2002

Mesonic Wavefunctions in the three-dimensional Gross-Neveu model

We present results from a numerical study of bound state wavefunctions in the (2+1)-dimensional Gross-Neveu model with staggered lattice fermions at both zero and nonzero temperature. Mesonic channels with varying quantum numbers are identified and analysed. In the strongly coupled chirally broken phase at T=0 the wavefunctions expose effects due to varying the interaction strength more effectively than straightforward spectroscopy. In the weakly coupled chirally restored phase information on fermion - antifermion scattering is recovered. In the hot chirally restored phase we find evidence for a screened interaction. The T=0 chirally symmetric phase is most readily distinguished from the symmetric phase at high T via the fermion dispersion relation.

hep-lat↗

arXiv2001

Lattice QCD at finite isospin density

We have simulated QCD at a finite chemical potential $μ_I$ for isospin ($I_3$) to probe part of the phase diagram for nuclear matter. Preliminary results suggest that for $μ_I > μ_c$, this theory forms a charged pion condensate which spontaneously breaks $I_3$, and the isospin density is non zero.

hep-lat↗

arXiv2001

The (2+1)-dimensional Gross-Neveu model with a U(1) chiral symmetry at non-zero temperature

We present results from numerical simulations of the (2+1)-dimensional Gross-Neveu model with a U(1) chiral symmetry and N_f=4 fermion species at non-zero temperature. We provide evidence that there are two different chirally symmetric phases, one critical and one with finite correlation length, separated by a Berezinskii-Kosterlitz-Thouless transition. We have also identified a regime above the critical temperature in which the fermions acquire a screening mass even in the absence of chiral symmetry breaking, analogous to the pseudogap behaviour observed in cuprate superconductors.

hep-lat↗

arXiv2001

Two-colour QCD at non-zero quark-number density

We have simulated two-colour four-flavour QCD at non-zero chemical potential $μ$ for quark number. Simulations were performed on $8^4$ and $12^3 \times 24$ lattices. Clear evidence was seen for the formation of a colourless diquark condensate which breaks quark number spontaneously, for $μ> μ_c \sim m_π/2$. The transition appears to be second order. We have measured the spectrum of scalar and pseudoscalar bosons which shows clear evidence for the expected Goldstone boson. Our results are in qualitative agreement with those from effective Lagrangians for the potential Goldstone excitations of this theory.

hep-lat↗

arXiv2001

Scaling behaviour at the $N_t=6$ chiral phase transition for 2-flavour lattice QCD with massless staggered quarks, and an irrelevant 4-fermion interaction

We have simulated lattice QCD with 2 flavours of massless staggered quarks. An irrelevant chiral 4-fermion interaction was added to the standard quark action to allow us to simulate at zero quark mass. Thermodynamics was studied on lattices of temporal extent 6. Clear evidence for a second order chiral transition was observed and the critical exponents $β_{mag}$, $δ$, $ν$ and $γ_{mag}$ were measured. These exponents did not agree with those expected by standard universality arguments. They were, however, consistent with tricritical behaviour. The $π$ and $σ$ screening masses were measured and showed clear evidence for chiral symmetry restoration at this transition.

hep-lat↗

arXiv2001

QCD at small non-zero quark chemical potentials

We study the effects of small chemical potentials associated with the three light quark flavors in QCD. We use a low-energy effective field theory that solely relies on the symmetries of the QCD partition function. We find three different phases: a normal phase, a pion superfluid phase and a kaon superfluid phase. The two superfluid phases are separated by a first order phase transition, whereas the normal phase and either of the superfluid phases are separated by a second order phase transition. We compute the quark-antiquark condensate, the pion condensate and the kaon condensate in each phase, as well as the isospin density, the strangeness density, and the mass spectrum.

hep-ph↗

arXiv2000

Two-colour QCD at finite fundamental quark-number density and related theories

We are simulating SU(2) Yang-Mills theory with four flavours of dynamical quarks in the fundamental representation of SU(2) `colour' at finite chemical potential, mu for quark number, as a model for QCD at finite baryon number density. In particular we observe that for mu large enough this theory undergoes a phase transition to a state with a diquark condensate which breaks quark-number symmetry. In this phase we examine the spectrum of light scalar and pseudoscalar bosons and see evidence for the Goldstone boson associated with this spontaneous symmetry breaking. This theory is closely related to QCD at finite chemical potential for isospin, a theory which we are now studying for SU(3) colour.

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