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J. B. Kogut

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

At least 73 records · Page 4Linked to original sources
arXiv2000

Chiral symmetry restoration in the three-dimensional four-fermion model at non-zero temperature and density

The three-dimensional four-fermion model with a Z_2 chiral symmetry and N=4 fermion species in the system is investigated numerically at non-zero temparature and chemical potential. The phase diagram in the (chemical potential, temperature) plane is mapped out quantitatively. A detailed finite size scaling analysis shows that the zero temperature and non-zero chemical potential chiral phase transition is first order, whereas the non-zero temperature and non-zero chemical potential transition remains second order down to very low temperatures. Quantitative results for the location of the end of the first order line are given. The simulations at T=0 provided no evidence for a nuclear liquid-gas transition.

hep-lat↗
arXiv2000

On the Triviality of Textbook Quantum Electrodynamics

By adding a small, irrelevant four fermi interaction to the action of lattice Quantum Electrodynamics (QED), the theory can be simulated with massless quarks in a vacuum free of lattice monopoles. This allows an ab initio high precision, controlled study of the existence of "textbook" Quantum Electrodynamics with several species of fermions. The lattice theory possesses a second order chiral phase transition which we show is logarithmically trivial. The logarithms of triviality, which modify mean field scaling laws, are pinpointed in several observables. The result supports Landau's contention that perturbative QED suffers from complete screening and would have a vanishing fine structure constant in the absence of a cutoff.

hep-lat↗
arXiv2000

QCD-like Theories at Finite Baryon Density

We study QCD-like theories with pseudoreal fermions at finite baryon density. Such theories include two-color QCD with quarks in the fundamental representation of the color group as well as any-color QCD with quarks in the adjoint color representation. In all such theories the lightest baryons are diquarks. At zero chemical potential $μ$ they are, together with the pseudoscalar mesons, the Goldstone modes of a spontaneously broken enlarged chiral symmetry group. Using symmetry principles, we derive the low-energy effective Lagrangian for these particles. We find that a second order phase transition occurs at a value of $μ$ equal to half the mass of the Goldstone modes. For values of $μ$ beyond this point the scalar diquarks Bose condense and the diquark condensate is nonzero. We calculate the dependence of the chiral condensate, the diquark condensate, the baryon charge density, and the masses of the diquark and pseudoscalar excitations on $μ$ at finite bare quark mass and scalar diquark source. The relevance of our results to lattice QCD calculations and to real three-color QCD at finite baryon density is discussed.

hep-ph↗
arXiv2000

Tricritical scaling at the N_t=6 chiral phase transition for 2 flavour lattice QCD with staggered quarks

We have simulated lattice QCD directly in the chiral limit of zero quark mass by adding an additional, irrelevant 4-fermion interaction to the standard action. Using lattices having temporal extent of six and spatial extents of twelve and eighteen, we find that the theory with 2 massless staggered quark flavors has a second order finite temperature phase transition. The critical exponents $β_{mag}$, $δ$ and $ν$ are measured and favour tricritical behaviour over that expected by universality arguments. The pion screening mass is consistent with zero below the transition, but is degenerate with the nonzero $σ(f_0)$ mass above the transition, indicating the restoration of chiral symmetry.

hep-lat↗
arXiv1999

On two-color QCD with baryon chemical potential

We study SU(2) color QCD with even number of quark flavors. First, using QCD inequalities we show that at finite baryon chemical potential mu, condensation must occur in the channel with scalar diquark quantum numbers. This breaks the U(1) symmetry generated by baryon charge (baryon superconductivity). Then we derive the effective Lagrangian describing low lying meson and baryon excitations using extended local chiral symmetry of the theory. This enables us to determine the leading term in the dependence of the masses on mu exactly.

hep-ph↗
arXiv1998

Critical region of the finite temperature chiral transition

We study a Yukawa theory with spontaneous chiral symmetry breaking and with a large number N of fermions near the finite temperature phase transition. Critical properties in such a system can be described by the mean field theory very close to the transition point. We show that the width of the region where non-trivial critical behavior sets in is suppressed by a certain power of 1/N. Our Monte Carlo simulations confirm these analytical results. We discuss implications for the chiral phase transition in QCD.

hep-lat↗
arXiv1998

Thermodynamics of Lattice QCD with 2 Quark Flavours: Chiral Symmetry and Topology

We have studied the restoration of chiral symmetry in lattice QCD at the finite temperature transition from hadronic matter to a quark-gluon plasma. By measuring the screening masses of flavour singlet and non-singlet meson excitations, we have seen evidence that, although flavour chiral symmetry is restored at this transition, flavour singlet (U(1)) axial symmetry is not. We conclude that this indicates that instantons continue to play an important role in the quark-gluon plasma phase.

hep-lat↗
arXiv1998

Thermodynamics of Lattice QCD with Chiral 4-Fermion Interactions

We have studied lattice QCD with an additional, irrelevant 4-fermion interaction having a U(1)xU(1) chiral symmetry, at finite temperatures. Adding this 4-fermion term allowed us to work at zero quark mass, which would have otherwise been impossible. The theory with 2 massless staggered quark flavours appears to have a first order finite temperature phase transition at N_t=4 for the value of 4-fermion coupling we have chosen, in contrast to what is expected for 2-flavour QCD. The pion screening mass is seen to vanish below this transition, only to become massive and degenerate with the sigma (f_0) above this transition where the chiral symmetry is restored, as is seen by the vanishing of the chiral condensate.

hep-lat↗
arXiv1998

Topology, fermionic zero modes and flavor singlet correlators in finite temperature QCD

We compute the screening correlators in the sigma and eta' flavor singlet channels in finite temperature QCD with 2 light quark flavors. Together with the correlators in the pi and delta channels, these are used to discuss several issues related to symmetry restoration and the nature of the QCD phase transition. Our calculations span a range of temperature extending from approximately 125 MeV to 170 MeV and are carried out in the context of a staggered fermion formulation on a 16^3x8 lattice. In addition to the computation at a fixed quark mass (am_q=0.00625), we discuss the issue of the chiral limit. After careful consideration of the zero-mode shift lattice artefact, we present rather strong (topological) arguments in favor of the non-restoration of U_A(1) at T_c.

hep-lat↗
arXiv1997

Results on Finite Density QCD

A brief summary of the formulation of QCD at finite chemical potental, $μ$, is presented. The failure of the quenched approximation to the problem is reviewed. Results are presented for dynamical simulations of the theory at strong and intermediate couplings. We find that the problems associated with the quenched theory persist: the onset of non-zero quark number does seem to occur at a chemical potential $\approx { {m_π} \over 2}$. However analysis of the Lee-Yang zeros of the grand canonical partition function in the complex fugacity plane, ($e^{μ/T}$), does show signals of critical behaviour in the expected region of chemical potential. Results are presented for a simulation at finite density of the Gross-Neveu model on a $16^3$ lattice near to the chiral limit. Contrary to our simulations of QCD no pathologies were found when $μ$ passed through the value $m_π/2}$.

hep-lat↗
arXiv1997

The Critical Points of Strongly Coupled Lattice QCD at Nonzero Chemical Potential

We study QCD at non-zero quark density, zero temperature, infinite coupling using the Glasgow algorithm. An improved complex zero analysis gives a critical point μ_c in agreement with that of chiral symmetry restoration computed with strong coupling expansions, and monomer-dimer simulations. We observe, however, two unphysical critical points: the onset for the number density μ_o, and μ_s the saturation threshold, coincident with pathological onsets observed in past quenched QCD calculations. An analysis of the probability distributions for particle number supports our physical interpretation of the critical point μ_c, and offers a new intepretation of μ_o, which confirms its unphysical nature. The perspectives for future lattice QCD calculations of the properties of dense baryonic matter are briefly discussed.

hep-lat↗
arXiv1996

Thermodynamics of lattice QCD with two light quark flavours on a 16^3 x 8 lattice II

We have extended our earlier simulations of the high temperature behaviour of lattice QCD with two light flavours of staggered quarks on a $16^3 \times 8$ lattice to lower quark mass (m_q=0.00625). The transition from hadronic matter to a quark-gluon plasma is observed at $6/g^2=5.49(2)$ corresponding to a temperature of $T_c \approx 140$MeV. We present measurements of observables which probe the nature of the quark-gluon plasma and serve to distinguish it from hadronic matter. Although the transition is quite abrupt, we have seen no indications that it is first order.

hep-lat↗
arXiv1996

Phase Structure of Lattice QCD at Finite Density with Dynamical Fermions

We compare the chemical potential associated with the onset of non-zero baryon number density on $6^4$ and $8^4$ lattices at $β=5.1$ and ma=0.01. We provide evidence for $Z(3)$ tunnelling. We determine a critical chemical potential of $μa \simeq 0.1$ which is unexpectedly low. We also determine the dependence of the onset of the observed phase transition on the quark mass. The physically misleading result of the quenched theory is shown to persist despite the inclusion of the complex fermion determinant.

hep-lat↗
arXiv1996

Manifestations of the axial anomaly in finite temperature QCD

We compute the flavor singlet meson correlators and screening masses in quenched and $N_f=2$ QCD at $N_t=8$. The consequences of our results for the realization of the $U_A(1)$ symmetry at finite T are discussed and an interpretation of our measurements in terms of the behaviour of the low lying fermionic modes is proposed.

hep-lat↗
arXiv1996

QCD with chiral 4-fermion interactions ($χ$QCD)

Lattice QCD with staggered quarks is augmented by the addition of a chiral 4-fermion interaction. The Dirac operator is now non-singular at $m_q=0$, decreasing the computing requirements for light quark simulations by at least an order of magnitude. We present preliminary results from simulations at finite and zero temperatures for $m_q=0$, with and without gauge fields.

hep-lat↗
arXiv1995

Pathologies of Quenched Lattice QCD at non--zero Density and its Effective Potential

We simulate lattice QCD at non--zero baryon density and zero temperature in the quenched approximation, both in the scaling region and in the infinite coupling limit. We investigate the nature of the forbidden region -- the range of chemical potential where the simulations grow prohibitively expensive, and the results, when available, are puzzling if not unphysical. At weak coupling we have explored the sensitivity of these pathologies to the lattice size, and found that using a large lattice ($64 \times 16^3$) does not remove them. The effective potential sheds considerable light on the problems in the simulations, and gives a clear interpretation of the forbidden region. The strong coupling simulations were particularly illuminating on this point.

hep-lat↗