431 research outputs found
The Lattice NJL Model at Non-zero Baryon and Isospin Densities
We present initial results of a numerical investigation of the chiral
symmetry restoring transition in the (3+1)-dimensional Nambu -- Jona-Lasinio
model with both non-zero baryon chemical potential (mu_B) and isospin chemical
potential (mu_I). With non-zero isospin chemical potential, the model suffers
from a sign problem. We proceed in two ways: (i) We perform ``partially
quenched'' simulations in which mu_I is made non-zero only during the
measurement of chiral observables; (ii) We perform full simulations with
imaginary isospin chemical potential with the aim to analytically continue
results to real mu_I.Comment: 3 pages, 3 figures, poster presented at LATTICE 2004, Fermi National
Accelerator Laboratory, June 21-26, 200
Electromagnetic Self-Duality in a Lattice Model
We formulate a Euclidean lattice theory of interacting elementary spin-half
electric and magnetic charges, which we refer to as electrons and magnetic
monopoles respectively. The model uses the polymer representation of the
fermion determinant, and exhibits a self-dual symmetry provided electric charge
and magnetic charge obey the minimal Dirac quantisation condition
. In a hopping parameter expansion at lowest order, we show that
virtual electron and monopole loops contribute radiative corrections of
opposite sign to the photon propagator. We argue that in the limit ,
fermion mass , the model describes QED together with strongly
interacting monopoles whose chiral symmetry is spontaneously broken. Prospects
for the existence of an interacting continuum limit at the self-dual point
are discussed.Comment: 29 pages plain TeX, 2 PostScript figures included using psfi
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.Comment: 18 page
Lattice QCD at finite T and \mu
Recent results of lattice QCD at finite temperature and density are reviewed.
At vanishing density the transition temperature, the equation of state and
hadron properties are discussed both for the pure gauge theory and for
dynamical staggered, Wilson and overlap fermions. The second part deals with
finite density. There are recent results for full QCD at finite temperature and
moderate density, while at larger densities QCD-like models are studied.Comment: 14 pages, 19 figures, lattice2003(plenary). Minor correction
QCD at non-zero temperature and density from the lattice
The study of systems as diverse as the cores of neutron stars and heavy-ion
collision experiments requires the understanding of the phase structure of QCD
at non-zero temperature, T, and chemical potential, mu_q. We review some of the
difficulties of performing lattice simulations of QCD with non-zero mu_q, and
outline the re-weighting method used to overcome this problem. This method is
used to determine the critical endpoint of QCD in the (mu_q,T) plane. We study
the pressure and quark number susceptibility at small mu_q.Comment: 5 pages, talk presented by C.R. Allton at the QCD Downunder
Conference, Barossa Valley and Adelaide, March 200
Compositeness, Triviality and Bounds on Critical Exponents for Fermions and Magnets
We argue that theories with fundamental fermions which undergo chiral
symmetry breaking have several universal features which are qualitatively
different than those of theories with fundamental scalars. Several bounds on
the critical indices and follow. We observe that in four
dimensions the logarithmic scaling violations enter into the Equation of State
of scalar theories, such as , and fermionic models, such as
Nambu-Jona-Lasinio, in qualitatively different ways. These observations lead to
useful approaches for analyzing lattice simulations of a wide class of model
field theories. Our results imply that {\it cannot} be a good
guide to understanding the possible triviality of spinor .Comment: 12 pages, 3 figures (not included), ILL-(TH)-93-2
Behavior of Hadrons at Finite Density -- Lattice Study of Color SU(2) QCD
Using two-color lattice QCD with Wilson fermions, we report a study of the
finite baryon number density system with two-flavors. First we investigate the
Polyakov line and thermodynamical uantities in the plane, where
and are the hopping parameter and chemical potential in the
fermion action, respectively. Then we calculate propagators of meson
() and baryon () states. We find that the vector
meson propagators are strongly modified in large regions, indicating the
reduction of the mass. This anomalous behavior of the vector meson is observed
for the first time in lattice QCD.Comment: 8 pages, 9 figures. References updated. To appear in Phys. Lett.
High Density Effective Theory Confronts the Fermi Liquid
The high density effective theory recently introduced by Hong and Hsu to
describe ultradense relativistic fermionic matter is used to calculate the
tree-level forward scattering amplitude between two particles at the Fermi
surface. While the direct term correctly reproduces that of the underlying
gauge theory, the exchange term has the wrong sign. The physical consequences
are discussed in the context of Landau's theoretical description of the Fermi
liquid.Comment: 15 pages, 2 figures; conclusion expanded, reference adde
Fluctuations in the quark-meson model for QCD with isospin chemical potential
We study the two-flavor quark-meson (QM) model with the functional
renormalization group (FRG) to describe the effects of collective mesonic
fluctuations on the phase diagram of QCD at finite baryon and isospin chemical
potentials, and . With only isospin chemical potential there is
a precise equivalence between the competing dynamics of chiral versus pion
condensation and that of collective mesonic and baryonic fluctuations in the
quark-meson-diquark model for two-color QCD at finite baryon chemical
potential. Here, finite introduces an additional dimension to the
phase diagram as compared to two-color QCD, however. At zero temperature, the
()-plane of this phase diagram is strongly constrained by the
"Silver Blaze problem." In particular, the onset of pion condensation must
occur at , independent of as long as
stays below the constituent quark mass of the QM model or the liquid-gas
transition line of nuclear matter in QCD. In order to maintain this relation
beyond mean field it is crucial to compute the pion mass from its timelike
correlator with the FRG in a consistent way.Comment: 10 pages, 11 figures; matches published versio
Looking for the Logarithms in Four-Dimensional Nambu-Jona-Lasinio Models
We study the problem of triviality in the four dimensional Nambu-Jona-Lasinio
model with discrete chiral symmetry using both large-N expansions and lattice
simulations. We find that logarithmic corrections to scaling appear in the
equation of state as predicted by the large-N expansion. The data from
lattice simulations is sufficiently accurate to distinguish logarithmically
trivial scaling from power law scaling. Simulations on different lattice sizes
reveal an interesting interplay of finite size effects and triviality. We argue
that such effects are qualitatively different for theories based on fundamental
scalar rather than fermion fields. Several lessons learned here can be applied
to simulations and analyses of more challenging field theories.Comment: 25 pages, 14 ps figure
- …