295 research outputs found
Logarithmic Corrections to the Equation of State in the SU(2)xSU(2) Nambu - Jona-Lasinio Model
We present results from a Monte Carlo simulation of the Nambu - Jona-Lasinio
model, with continuous SU(2)xSU(2) chiral symmetry, in four Euclidean
dimensions. Different model equations of state, corresponding to different
theoretical scenarios, are tested against the order parameter data. The results
are sensitive to necessary assumptions about the shape and extent of the
scaling region. Our best fits favour a trivial scenario in which the
logarithmic corrections are qualitatively similar to those predicted by the
large N_f approximation. This is supported by a separate analysis of finite
volume corrections for data taken directly in the chiral limit.Comment: 37 pages LaTeX (RevTeX) including 12 .eps figure
Four - Fermi Theories in Fewer Than Four Dimensions
Four-fermi models in dimensionality exhibit an ultra-violet stable
renormalization group fixed point at a strong value of the coupling constant
where chiral symmetry is spontaneously broken. The resulting field theory
describes relativistic fermions interacting non-trivially via exchange of
scalar bound states. We calculate the corrections to this picture,
where is the number of fermion species, for a variety of models and
confirm their renormalizability to this order. A connection between
renormalizability and the hyperscaling relations between the theory's critical
exponents is made explicit. We present results of extensive numerical
simulations of the simplest model for , performed using the hybrid Monte
Carlo algorithm on lattice sizes ranging from to . For
species of massless fermions we confirm the existence of a second order phase
transition where chiral symmetry is spontaneously broken. Using both direct
measurement and finite size scaling arguments we estimate the critical
exponents , , and . We also investigate symmetry
restoration at non-zero temperature, and the scalar two-point correlation
function in the vicinity of the bulk transition. All our results are in
excellent agreement with analytic predictions, and support the contention that
the expansion is accurate for this class of models.Comment: CERN-TH.6557/92 ILL-(TH)-92-\# 19, 60 pages, 18 figures (not
included
Non-Perturbative Renormalization Group Flows in Two-Dimensional Quantum Gravity
Recently a block spin renormalization group approach was proposed for the
dynamical triangulation formulation of two-dimensional quantum gravity. We use
this approach to examine non-perturbatively a particular class of higher
derivative actions for pure gravity.Comment: 17 page
The Phase Diagram of Four Flavor SU(2) Lattice Gauge Theory at Nonzero Chemical Potential and Temperature
SU(2) lattice gauge theory with four flavors of quarks is simulated at
nonzero chemical potential and temperature and the results are
compared to the predictions of Effective Lagrangians. Simulations on
lattices indicate that at zero the theory experiences a second order phase
transition to a diquark condensate state. Several methods of analysis,
including equation of state fits suggested by Chiral Perturbation Theory,
suggest that mean-field scaling describes this critical point. Nonzero and
are studied on lattices. For low , increasing
takes the system through a line of second order phase transitions to a diquark
condensed phase. Increasing at high , the system passes through a line
of first order transitions from the diquark phase to the quark-gluon plasma
phase. Metastability is found in the vicinity of the first order line. There is
a tricritical point along this line of transitions whose position is consistent
with theoretical predictions.Comment: 42 pages revtex, 25 figures postscrip
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.Comment: reference to Phys. Rev. Lett.80, 4119(1998) adde
Diquark Condensation at Nonzero Chemical Potential and Temperature
SU(2) lattice gauge theory with four flavors of quarks is studied at nonzero
chemical potential and temperature by computer simulation and
Effective Lagrangian techniques. Simulations are done on ,
and lattices and the diquark condensate, chiral order
parameter, Wilson line, fermion energy and number densities are measured.
Simulations at a fixed, nonzero quark mass provide evidence for a tricritical
point in the - plane associated with diquark condensation. For low ,
increasing takes the system through a line of second order phase
transitions to a diquark condensed phase. Increasing at high , the
system passes through a line of first order transitions from the diquark phase
to the quark-gluon plasma phase. Using Effective Lagrangians we estimate the
position of the tricritical point and ascribe its existence to trilinear
couplings that increase with and .Comment: 18 pages revtex, 11 figures postscrip
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