405 research outputs found
Interplay of universality classes in a three-dimensional Yukawa model
We investigate numerically on the lattice the interplay of universality
classes of the three-dimensional Yukawa model with U(1) chiral symmetry, using
the Binder method of finite size scaling. At zero Yukawa coupling the scaling
related to the magnetic Wilson--Fisher fixed point is confirmed. At
sufficiently strong Yukawa coupling the dominance of the chiral fixed point
associated with the 3D Gross--Neveu model is observed for various values of the
coupling parameters, including infinite scalar selfcoupling. In both cases the
Binder method works consistently in a broad range of lattice sizes. However,
when the Yukawa coupling is decreased the finite size behavior gets complicated
and the Binder method gives inconsistent results for different lattice sizes.
This signals a cross-over between the universality classes of the two fixed
points.Comment: 24 pp. LaTeX 2e src, needs psfig.st
Magnetic and chiral universality classes in a 3D Yukawa model
The 3D Yukawa model with U(1) chiral symmetry is investigated in a broad
interval of parameters using the Binder method. Critical exponents of the
Wilson-Fisher (magnetic) and Gross-Neveu (chiral) universality classes are
measured. The model is dominated by the chiral universality class. However at
weak coupling we observe a crossover between both classes, manifested by
difficulties with the Binder method which otherwise works well.Comment: 4 pages, contribution to LATTICE 9
Strongly coupled lattice gauge theory with dynamical fermion mass generation in three dimensions
We investigate the critical behaviour of a three-dimensional lattice
\chiU\phi_3 model in the chiral limit. The model consists of a staggered
fermion field, a U(1) gauge field (with coupling parameter ) and a
complex scalar field (with hopping parameter ). Two different methods
are used: 1) fits of the chiral condensate and the mass of the neutral
unconfined composite fermion to an equation of state and 2) finite size scaling
investigations of the Lee-Yang zeros of the partition function in the complex
fermion mass plane. For strong gauge coupling () the critical
exponents for the chiral phase transition are determined. We find strong
indications that the chiral phase transition is in one universality class in
this interval: that of the three-dimensional Gross-Neveu model with two
fermions. Thus the continuum limit of the \chiU\phi_3 model defines here a
nonperturbatively renormalizable gauge theory with dynamical mass generation.
At weak gauge coupling and small , we explore a region in which the
mass in the neutral fermion channel is large but the chiral condensate on
finite lattices very small. If it does not vanish in the infinite volume limit,
then a continuum limit with massive unconfined fermion might be possible in
this region, too.Comment: 27 pages, 16 figure
Study of the Asymptotic Freedom of 2D Yukawa Models on the Lattice
We investigate on the lattice the Yukawa models in 2 dimensions with Z(2) and
U(1) symmetries. These models reduce to the usual and chiral Gross-Neveu
models, respectively, when the kinetic and the selfcoupling terms of the scalar
field are turned off. The numerical data and mean field arguments suggest that,
at least for some range of the scalar field hopping parameter, fermion mass is
dynamically generated for arbitrarily weak Yukawa coupling. The models are
asymptotically free in this coupling, like the Gross-Neveu models, even when
the scalar quartic selfcoupling is strong.Comment: LaTeX, 11 pages (including 4 postscript figures); OUTP-93-01P (HLRZ
93-15
On the equivalence between 2D Yukawa and Gross-Neveu models
We study numerically on the lattice the 2D Yukawa model with the U(1) chiral
symmetry and = 16 at infinite scalar field self-coupling. The scaling
behaviour of the fermion mass, as the Yukawa coupling approaches zero, is
analysed using the mean field method. It is found to agree with that of the
Gross-Neveu model with the same symmetry and . The results suggest that
the 2D Yukawa models belong to the universality class of the Gross-Neveu models
not only at weak scalar field self-coupling but also for a broad range of the
bare parameters which is not accessible to the expansion. New
universality classes might arise at the crossover to the spin model
universality class, however.Comment: 18 pages, Juelich HLRZ 111/9
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
Two-dimensional model of dynamical fermion mass generation in strongly coupled gauge theories
We generalize the Schwinger model on the lattice by adding a charged
scalar field. In this so-called model the scalar field shields
the fermion charge, and a neutral fermion, acquiring mass dynamically, is
present in the spectrum. We study numerically the mass of this fermion at
various large fixed values of the gauge coupling by varying the effective
four-fermion coupling, and find an indication that its scaling behavior is the
same as that of the fermion mass in the chiral Gross-Neveu model. This suggests
that the model is in the same universality class as the
Gross-Neveu model, and thus renormalizable and asymptotic free at arbitrary
strong gauge coupling.Comment: 18 pages, LaTeX2e, requires packages rotating.sty and curves.sty from
CTA
Critical exponents of the Gross-Neveu model from the effective average action
The phase transition of the Gross-Neveu model with N fermions is investigated
by means of a non-perturbative evolution equation for the scale dependence of
the effective average action. The critical exponents and scaling amplitudes are
calculated for various values of N in d=3. It is also explicitely verified that
the Neveu-Yukawa model belongs to the same universality class as the
Gross-Neveu model.Comment: RevTeX, 4 pages, 2 figures, 1 table. Typos corrected in equation
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
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