107 research outputs found
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
The nature of the continuum limit in strongly coupled quenched QED
We review the results of large scale simulations of noncompact quenched
which use spectrum and Equation of State calculations to determine the theory's
phase diagram, critical indices, and continuum limit. The resulting anomalous
dimensions are in good agreement with Schwinger-Dyson solutions of the ladder
graphs of conventional and they satisfy the hyperscaling relations
expected of a relativistic renormalizable field theory. The spectroscopy
results satisfy the constraints of the Goldstone mechanism and PCAC, and may be
indicative of Technicolor versions of the Standard Model which are strongly
coupled at short distances.Comment: (talk given at the XXVI ICHEP, Dallas, TX, Aug 6-12 92), 6 pp.,
ILL-(TH)-92-#2
Spectroscopy, Equation Of State And Monopole Percolation In Lattice QED With Two Flavors
Non-compact lattice QED with two flavors of light dynamical quarks is
simulated on lattices, and the chiral condensate, monopole density and
susceptibility and the meson masses are measured. Data from relatively high
statistics runs at relatively small bare fermion masses of 0.005, 0.01, 0.02
and 0.03 (lattice units) are presented. Three independent methods of data
analysis indicate that the critical point occurs at and that
the monopole condensation and chiral symmetry breaking transitions are
coincident. The monopole condensation data satisfies finite size scaling
hypotheses with critical indices compatible with four dimensional percolation.
The best chiral equation of state fit produces critical exponents
(, ) which deviate significantly from mean
field expectations. Data for the ratio of the sigma to pion masses produces an
estimate of the critical index in good agreement with chiral
condensate measurements. In the strong coupling phase the ratio of the meson
masses are ,
and , while on the weak coupling side of the
transition , ,
indicating the restoration of chiral symmetry.\footnote{\,^{}}{August 1992}Comment: 21 pages, 24 figures (not included
Kosterlitz-Thouless Universality in a Fermionic System
A new extension of the attractive Hubbard model is constructed to study the
critical behavior near a finite temperature superconducting phase transition in
two dimensions using the recently developed meron-cluster algorithm. Unlike
previous calculations in the attractive Hubbard model which were limited to
small lattices, the new algorithm is used to study the critical behavior on
lattices as large as . These precise results for the first time
show that a fermionic system can undergo a finite temperature phase transition
whose critical behavior is well described by the predictions of Kosterlitz and
Thouless almost three decades ago. In particular it is confirmed that the
spatial winding number susceptibility obeys the well known predictions of
finite size scaling for and up to logarithmic corrections the pair
susceptibility scales as at large volumes with for .Comment: Revtex format; 4 pages, 2 figure
Dimensional Reduction and Quantum-to-Classical Reduction at High Temperatures
We discuss the relation between dimensional reduction in quantum field
theories at finite temperature and a familiar quantum mechanical phenomenon
that quantum effects become negligible at high temperatures. Fermi and Bose
fields are compared in this respect. We show that decoupling of fermions from
the dimensionally reduced theory can be related to the non-existence of
classical statistics for a Fermi field.Comment: 11 pages, REVTeX, revised v. to be published in Phys. Rev. D: some
points made more explici
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.Comment: 18 page
On the Interplay of Monopoles and Chiral Symmetry Breaking in Non-Compact Lattice QED
Non-compact lattice QED is simulated for various numbers of fermion species
ranging from 8 through 40 by the exact Hybrid Monte Carlo algorithm. Over
this range of , chiral symmetry breaking is found to be strongly
correlated with the effective monopoles in the theory. For between 8 and
16 the chiral symmetry breaking and monopole percolation transitions are second
order and coincident. Assuming powerlaw critical behavior, the correlation
length exponent for the chiral transition is identical to that of monopole
percolation. This result supports the conjecture that monopole percolation
``drives" the nontrivial chiral transition. For between 20 and 32, the
monopoles experience a first order condensation transition coincident with a
first order chiral transition. For as large as 40 both transitions are
strongly suppressed. The data at large N_f (N_f \mathrel {\mathpalette \vereq
>} 20) is interpreted in terms of a strongly interacting monopole gas-liquid
transition.Comment: Revtex file, 23 pages, hardcopy figures only
On the Logarithmic Triviality of Scalar Quantum Electrodynamics
Using finite size scaling and histogram methods we obtain numerical results
from lattice simulations indicating the logarithmic triviality of scalar
quantum electrodynamics, even when the bare gauge coupling is chosen large.
Simulations of the non-compact formulation of the lattice abelian Higgs model
with fixed length scalar fields on lattices with ranging from
through indicate a line of second order critical points.
Fluctuation-induced first order transitions are ruled out. Runs of over ten
million sweeps for each produce specific heat peaks which grow
logarithmically with and whose critical couplings shift with picking
out a correlation length exponent of consistent with mean field
theory. This behavior is qualitatively similar to that found in pure
.Comment: 9 page
- …