264 research outputs found
QCD with Adjoint Scalars in 2D: Properties in the Colourless Scalar Sector
We present a numerical study of an SU(3) gauged 2D model for adjoint scalar
fields, defined by dimensional reduction of pure gauge QCD in (2+1)D at high
temperature. In the symmetric phase of its global Z_2 symmetry, two colourless
boundstates, even and odd under Z_2, are identified. Their respective
contributions (poles) in correlation functions of local composite operators A_n
of degree n=2p and 2p+1 in the scalar fields (p=1,2) fulfill factorization. The
contributions of two particle states (cuts) are detected. Their size agrees
with estimates based on a meanfield-like decomposition of the p=2 operators
into polynomials in p=1 operators. No sizable signal in any A_n correlation can
be attributed to 1/n times a Debye screening length associated with n
elementary fields. These results are quantitatively consistent with the picture
of scalar ``matter'' fields confined within colourless boundstates whose
residual ``strong'' interactions are very weak.Comment: 27 pages, improved presentation of results and some references added,
as accepted by Nucl. Phys.
High Temperature 3D QCD: Dimensional Reduction at Work
We investigate the three-dimensional SU(3) gauge theory at finite temperature
in the framework of dimensional reduction. The large scale properties of this
theory are expected to be conceptually more complicated than in four
dimensions. The dimensionally reduced action is computed in closed analytical
form. The resulting effective two-dimensional theory is studied numerically
both in the electric and magnetic sector. We find that dimensional reduction
works excellently down to temperatures of 1.5 times the deconfinement phase
transition temperature and even on rather short length scales. We obtain strong
evidence that for , even at high temperature the colour averaged
potential is represented by the exchange of a single state, at variance with
the usual Debye screening picture involving a pair of electric gluons.Comment: 27 page
Lattice supersymmetry, superfields and renormalization
We study Euclidean lattice formulations of non-gauge supersymmetric models
with up to four supercharges in various dimensions. We formulate the conditions
under which the interacting lattice theory can exactly preserve one or more
nilpotent anticommuting supersymmetries. We introduce a superfield formalism,
which allows the enumeration of all possible lattice supersymmetry invariants.
We use it to discuss the formulation of Q-exact lattice actions and their
renormalization in a general manner. In some examples, one exact supersymmetry
guarantees finiteness of the continuum limit of the lattice theory. As a
consequence, we show that the desired quantum continuum limit is obtained
without fine tuning for these models. Finally, we discuss the implications and
possible further applications of our results to the study of gauge and
non-gauge models.Comment: 44 pages, 1 figur
The Asymptotic Expansion of Lattice Loop Integrals Around the Continuum Limit
We present a method of computing any one-loop integral in lattice
perturbation theory by systematically expanding around its continuum limit. At
any order in the expansion in the lattice spacing, the result can be written as
a sum of continuum loop integrals in analytic regularization and a few genuine
lattice integrals (``master integrals''). These lattice master integrals are
independent of external momenta and masses and can be computed numerically. At
the one-loop level, there are four master integrals in a theory with only
bosonic fields, seven in HQET and sixteen in QED or QCD with Wilson fermions.Comment: 9 pages, 2 figure
Critical Phenomena with Linked Cluster Expansions in a Finite Volume
Linked cluster expansions are generalized from an infinite to a finite
volume. They are performed to 20th order in the expansion parameter to approach
the critical region from the symmetric phase. A new criterion is proposed to
distinguish 1st from 2nd order transitions within a finite size scaling
analysis. The criterion applies also to other methods for investigating the
phase structure such as Monte Carlo simulations. Our computational tools are
illustrated at the example of scalar O(N) models with four and six-point
couplings for and in three dimensions. It is shown how to localize
the tricritical line in these models. We indicate some further applications of
our methods to the electroweak transition as well as to models for
superconductivity.Comment: 36 pages, latex2e, 7 eps figures included, uuencoded, gzipped and
tarred tex file hdth9607.te
Interpolation Parameter and Expansion for the Three Dimensional Non-Trivial Scalar Infrared Fixed Point
We compute the non--trivial infrared --fixed point by means of an
interpolation expansion in fixed dimension. The expansion is formulated for an
infinitesimal momentum space renormalization group. We choose a coordinate
representation for the fixed point interaction in derivative expansion, and
compute its coordinates to high orders by means of computer algebra. We compute
the series for the critical exponent up to order twenty five of
interpolation expansion in this representation, and evaluate it using \pade,
Borel--\pade, Borel--conformal--\pade, and Dlog--\pade resummation. The
resummation returns as the value of .Comment: 29 pages, Latex2e, 2 Postscript figure
Meron-cluster algorithms and chiral symmetry breaking in a (2+1)-d staggered fermion model
The recently developed Meron-Cluster algorithm completely solves the
exponentially difficult sign problem for a number of models previously
inaccessible to numerical simulation. We use this algorithm in a high-precision
study of a model of N=1 flavor of staggered fermions in (2+1)-dimensions with a
four-fermion interaction. This model cannot be explored using standard
algorithms. We find that the Z(2) chiral symmetry of this model is
spontaneously broken at low temperatures and that the finite-temperature chiral
phase transition is in the universality class of the 2-d Ising model, as
expected.Comment: 18 pages, LaTe
A Lattice Monte Carlo Study of the Hot Electroweak Phase Transition
We study the finite temperature electroweak phase transition with lattice
perturbation theory and Monte Carlo techniques. Dimensional reduction is used
to approximate the full four-dimensional SU(2) + a fundamental doublet Higgs
theory by an effective three-dimensional SU(2) + adjoint Higgs + fundamental
Higgs theory with coefficients depending on temperature via screening masses
and mass counterterms. Fermions contribute to the effective theory only via the
and dependence of the coefficients. For sufficiently small
lattices ( for = 35 GeV) the study of the one-loop lattice
effective potential shows the existence of the {\em second} order phase
transition even for the small Higgs masses. At the same time, a clear signal of
a {\em first order} phase transition is seen on the lattice simulations with a
transition temperature close to but less than the value determined from the
perturbative calculations. This indicates that the dynamics of the first order
electroweak phase transition depends strongly on non-perturbative effects and
is not exclusively related to the so-called term in the effective
potential.Comment: 15 pages, use latex+epsfig, includes 6 ps-figures, CERN-TH.6901/9
The Spatial String Tension in the Deconfined Phase of the (3+1)-Dimensional SU(2) Gauge Theory
We present results of a detailed investigation of the temperature dependence
of the spatial string tension in SU(2) gauge theory. We show, for the first
time, that the spatial string tension is scaling on the lattice and thus is
non-vanishing in the continuum limit. It is temperature independent below Tc
and rises rapidly above. For temperatures larger than 2Tc we find a scaling
behaviour consistent with sigma_s(T) = 0.136(11) g^4(T) T^2, where g(T) is the
2-loop running coupling constant with a scale parameter determined as Lambda_T
= 0.076(13) Tc.Comment: 8 pages (Latex, shell archive, 3 PostScript figures), HLRZ-93-43,
BI-TP 93/30, FSU-SCRI-93-76, WUB 93-2
Gauge Theories on a 2+2 Anisotropic Lattice
The implementation of gauge theories on a four-dimensional anisotropic
lattice with two distinct lattice spacings is discussed, with special attention
to the case where two axes are finely and two axes are coarsely discretized.
Feynman rules for the Wilson gauge action are derived and the renormalizability
of the theory and the recovery of the continuum limit are analyzed. The
calculation of the gluon propagator and the restoration of Lorentz invariance
in on-shell states is presented to one-loop order in lattice perturbation
theory for on both 2+2 and 3+1 lattices.Comment: 27 pages, uses feynmf. Font compatibility adjuste
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