45,054 research outputs found
Zero-temperature TAP equations for the Ghatak-Sherrington model
The zero-temperature TAP equations for the spin-1 Ghatak-Sherrington model
are investigated. The spin-glass energy density (ground state) is determined as
a function of the anisotropy crystal field for a large number of spins.
This allows us to locate a first-order transition between the spin-glass and
paramagnetic phases within a good accuracy. The total number of solutions is
also determined as a function of .Comment: 11 pages, 2 ps figures include
AdS/QCD, Light-Front Holography, and Sublimated Gluons
Gauge/gravity duality leads to a simple, analytical, and phenomenologically
compelling nonperturbative approximation to the full light-front QCD
Hamiltonian. This approach, called "Light-Front Holography", successfully
describes the spectroscopy of light-quark meson and baryons, their elastic and
transition form factors, and other hadronic properties. The bound-state
Schrodinger and Dirac equations of the soft-wall AdS/QCD model predict linear
Regge trajectories which have the same slope in orbital angular momentum L and
radial quantum number n for both mesons and baryons. Light-front holography
connects the fifth-dimensional coordinate of AdS space z to an invariant impact
separation variable zeta in 3+1 space at fixed light-front time. A key feature
is the determination of the frame-independent light-front wavefunctions of
hadrons -- the relativistic analogs of the Schrodinger wavefunctions of atomic
physics which allow one to compute form factors, transversity distributions,
spin properties of the valence quarks, jet hadronization, and other hadronic
observables. One thus obtains a one-parameter color-confining model for hadron
physics at the amplitude level. AdS/QCD also predicts the form of a
non-perturbative effective running coupling and its beta-function with an
infrared fixed point which agrees with the effective coupling extracted from
measurements of the Bjorken sum rule below 1 GeV^2. This is consistent with a
flux-tube interpretation of QCD where soft gluons are sublimated into a
color-confining potential for quarks. We discuss a number of phenomenological
hadronic properties which support this picture.Comment: Invited talk, presented by SJB at the International Workshop on QCD
Green's Functions, Confinement and Phenomenology, 5-9 September 2011, Trento,
Ital
Effects of Random Biquadratic Couplings in a Spin-1 Spin-Glass Model
A spin-1 model, appropriated to study the competition between bilinear
(J_{ij}S_{i}S_{j}) and biquadratic (K_{ij}S_{i}^{2}S_{j}^{2}) random
interactions, both of them with zero mean, is investigated. The interactions
are infinite-ranged and the replica method is employed. Within the
replica-symmetric assumption, the system presents two phases, namely,
paramagnetic and spin-glass, separated by a continuous transition line. The
stability analysis of the replica-symmetric solution yields, besides the usual
instability associated with the spin-glass ordering, a new phase due to the
random biquadratic couplings between the spins.Comment: 16 pages plus 2 ps figure
AdS/QCD, Light-Front Holography, and Color Confinement
A remarkable holographic feature of dynamics in AdS space in five dimensions
is that it is dual to Hamiltonian theory in physical space-time, quantized at
fixed light-front time {\tau} = t+z/c. This light-front holographic principle
provides a precise relation between the bound-state amplitudes in AdS space and
the boost-invariant light-front wavefunctions describing the internal structure
of hadrons in physical space-time. The fifth dimension coordinate z is dual to
the light front variable {\zeta} describing the invariant separation of the
quark constituents. The resulting valence Fock-state wavefunction
eigensolutions of the light-front QCD Hamiltonian satisfy a single-variable
relativistic equation of motion, analogous to the nonrelativistic radial
Schr\"odinger equation. The soft-wall dilaton profile exp ({\kappa}^2
{\zeta}^2) provides a model for the light-front potential which is
color-confining and reproduces well the linear Regge behavior of the
light-quark hadron spectrum in both L, the orbital angular momentum, and n, the
radial node number. The pion mass vanishes in the chiral limit and other
features of chiral symmetry are satisfied. The resulting running QCD coupling
displays an infrared fixed point. The elastic and transition form factors of
the pion and the nucleons are also found to be well described in this
framework. The light-front AdS/QCD holographic approach thus gives a
frame-independent analytic first approximation of the color-confining dynamics,
spectroscopy, and excitation spectra of relativistic light-quark bound states
in QCD.Comment: Contribution to the Proceedings of the conference, Xth Quark
Confinement and the Hadron Spectrum, October 8-12, 2012, TUM Campus Garching,
Munich, German
Effective restoration of chiral and axial symmetries at finite temperature and density
The effective restoration of chiral and axial symmetries is investigated
within the framework of the SU(3) Nambu-Jona-Lasinio model. The topological
susceptibility, modeled from lattice data at finite temperature, is used to
extract the temperature dependence of the coupling strength of the anomaly. The
study of the scalar and pseudoscalar mixing angles is performed in order to
discuss the evolution of the flavor combinations of pairs and its
consequences for the degeneracy of chiral partners. A similar study at zero
temperature and finite density is also realized.Comment: 5 pages, 1 figure. Talk given at Strange Quark Matter 2004, Cape
Town, South Africa, 15-20 September, 200
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