1,158 research outputs found
The Finite Temperature SU(2) Savvidy Model with a Non-trivial Polyakov Loop
We calculate the complete one-loop effective potential for SU(2) gauge bosons
at temperature T as a function of two variables: phi, the angle associated with
a non-trivial Polyakov loop, and H, a constant background chromomagnetic field.
Using techniques broadly applicable to finite temperature field theories, we
develop both low and high temperature expansions. At low temperatures, the real
part of the effective potential V_R indicates a rich phase structure, with a
discontinuous alternation between confined (phi=pi) and deconfined phases
(phi=0). The background field H moves slowly upward from its zero-temperature
value as T increases, in such a way that sqrt(gH)/(pi T) is approximately an
integer. Beyond a certain temperature on the order of sqrt(gH), the deconfined
phase is always preferred. At high temperatures, where asymptotic freedom
applies, the deconfined phase phi=0 is always preferred, and sqrt(gH) is of
order g^2(T)T. The imaginary part of the effective potential is non-zero at the
global minimum of V_R for all temperatures. A non-perturbative magnetic
screening mass of the form M_m = cg^2(T)T with a sufficiently large coefficient
c removes this instability at high temperature, leading to a stable
high-temperature phase with phi=0 and H=0, characteristic of a
weakly-interacting gas of gauge particles. The value of M_m obtained is
comparable with lattice estimates.Comment: 28 pages, 5 eps figures; RevTeX 3 with graphic
Induced Universal Properties and Deconfinement
We propose a general strategy to determine universal properties induced by a
nearby phase transition on a non-order parameter field. A general
renormalizable Lagrangian is used, which contains the order parameter and a
non-order parameter field, and respects all the symmetries present. We
investigate the case in which the order parameter field depends only on space
coordinates and the case in which this field is also time dependent. We find
that the spatial correlators of the non-order parameter field, in both cases,
are infrared dominated and can be used to determine properties of the phase
transition. We predict a universal behavior for the screening mass of a generic
singlet field, and show how to extract relevant information from such a
quantity. We also demonstrate that the pole mass of the non-order parameter
field is not infrared sensitive. Our results can be applied to any continuous
phase transition. As an example we consider the deconfining transition in pure
Yang-Mills theory, and show that our findings are supported by lattice data.
Our analysis suggests that monitoring the spatial correlators of different
hadron species, more specifically the derivatives of these, provides an
efficient and sufficient way to experimentally uncover the deconfining phase
transition and its features.Comment: Added computational details and improved the text. The results are
unchange
Quark number susceptibilities: lattice QCD versus PNJL model
Quark number susceptibilities at finite quark chemical potential are
investigated in the framework of the Polyakov-loop-extended Nambu Jona-Lasinio
(PNJL) model. A detailed comparison is performed between the available lattice
data, extrapolated using a Taylor expansion around vanishing chemical
potential, and PNJL results consistently obtained from a Taylor series
truncated at the same order. The validity of the Taylor expansion is then
examined through a comparison between the full and truncated PNJL model
calculations.Comment: 8 pages, 2 figure
QGP Susceptibilities from PNJL Model
An improved version of the PNJL model is used to calculate various
thermodynamical quantities, {\it viz.}, quark number susceptibility, isospin
susceptibility, specific heat, speed of sound and conformal measure. Comparison
with Lattice data is found to be encouraging.Comment: 4 pages, 2 figures, poster presented at Quark Matter'0
Universality in Random Walk Models with Birth and Death
Models of random walks are considered in which walkers are born at one
location and die at all other locations with uniform death rate. Steady-state
distributions of random walkers exhibit dimensionally dependent critical
behavior as a function of the birth rate. Exact analytical results for a
hyperspherical lattice yield a second-order phase transition with a nontrivial
critical exponent for all positive dimensions . Numerical studies
of hypercubic and fractal lattices indicate that these exact results are
universal. Implications for the adsorption transition of polymers at curved
interfaces are discussed.Comment: 11 pages, revtex, 2 postscript figure
Two-point functions for SU(3) Polyakov Loops near T_c
We discuss the behavior of two point functions for Polyakov loops in a SU(3)
gauge theory about the critical temperature, T_c. From a Z(3) model, in mean
field theory we obtain a prediction for the ratio of masses at T_c, extracted
from correlation functions for the imaginary and real parts of the Polyakov
loop. This ratio is m_i/m_r = 3 if the potential only includes terms up to
quartic order in the Polyakov loop; its value changes as pentic and hexatic
interactions become important. The Polyakov Loop Model then predicts how
m_i/m_r changes above T_c.Comment: 5 pages, no figures; reference adde
Phenomenological Equations of State for the Quark-Gluon Plasma
Two phenomenological models describing an SU(N) quark-gluon plasma are
presented. The first is obtained from high temperature expansions of the free
energy of a massive gluon, while the second is derived by demanding color
neutrality over a certain length scale. Each model has a single free parameter,
exhibits behavior similar to lattice simulations over the range T_d - 5T_d, and
has the correct blackbody behavior for large temperatures. The N = 2
deconfinement transition is second order in both models, while N = 3,4, and 5
are first order. Both models appear to have a smooth large-N limit. For N >= 4,
it is shown that the trace of the Polyakov loop is insufficient to characterize
the phase structure; the free energy is best described using the eigenvalues of
the Polyakov loop. In both models, the confined phase is characterized by a
mutual repulsion of Polyakov loop eigenvalues that makes the Polyakov loop
expectation value zero. In the deconfined phase, the rotation of the
eigenvalues in the complex plane towards 1 is responsible for the approach to
the blackbody limit over the range T_d - 5T_d. The addition of massless quarks
in SU(3) breaks Z(3) symmetry weakly and eliminates the deconfining phase
transition. In contrast, a first-order phase transition persists with
sufficiently heavy quarks.Comment: 22 pages, RevTeX, 9 eps file
Thermodynamics of the PNJL model
QCD thermodynamics is investigated by means of the Polyakov-loop-extended
Nambu Jona-Lasinio (PNJL) model, in which quarks couple simultaneously to the
chiral condensate and to a background temporal gauge field representing
Polyakov loop dynamics. The behaviour of the Polyakov loop as a function of
temperature is obtained by minimizing the thermodynamic potential of the
system. A Taylor series expansion of the pressure is performed. Pressure
difference and quark number density are then evaluated up to sixth order in
quark chemical potential, and compared to the corresponding lattice data. The
validity of the Taylor expansion is discussed within our model, through a
comparison between the full results and the truncated ones.Comment: 6 pages, 5 figures, Talk given at the Workshop for Young Scientists
on the Physics of Ultrarelativistic Nucleus-Nucleus Collisions (Hot Quarks
2006), Villasimius, Italy, 15-20 May 200
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