1,477 research outputs found
Linked Cluster Expansions on non-trivial topologies
Linked cluster expansions provide a useful tool both for analytical and
numerical investigations of lattice field theories. The expansion parameter is
the interaction strength fields at neighboured lattice sites are coupled. They
result into convergent series for free energies, correlation functions and
susceptibilities. The expansions have been generalized to field theories at
finite temperature and to a finite volume. Detailed information on critical
behaviour can be extracted from the high order behaviour of the susceptibility
series. We outline some of the steps by which the 20th order is achieved.Comment: 3 pages, Talk presented at LATTICE96(Theoretical Developments
Chiral symmetry restoration of QCD and the Gross-Neveu model
Two flavour massless QCD has a second order chiral transition which has been
argued to belong to the universality class of the O(4) spin model. The
arguments have been questioned recently, and the transition was claimed to be
mean field behaved. We discuss this issue at the example of the
Gross-Neveu model. A solution is obtained by applying various well established
analytical methods.Comment: LATTICE98(hightemp
Finite Size Scaling Analysis with Linked Cluster Expansions
Linked cluster expansions are generalized from an infinite to a finite volume
on a -dimensional hypercubic lattice. They are performed to 20th order in
the expansion parameter to investigate the phase structure of scalar
models for the cases of and in 3 dimensions. In particular we
propose a new criterion to distinguish first from second order transitions via
the volume dependence of response functions for couplings close to but not at
the critical value. The criterion is applicable to Monte Carlo simulations as
well. Here it is used to localize the tricritical line in a
theory. We indicate further applications to the electroweak transition.Comment: 3 pages, 1 figure, Talk presented at LATTICE96(Theoretical
Developments
Hopping Parameter Series Construction for Models with Nontrivial Vacuum
Hopping parameter expansions are convergent power series. Under general
conditions they allow for the quantitative investigation of phase transition
and critical behaviour. The critical information is encoded in the high order
coefficients. Recently, 20th order computations have become feasible and used
for a large class of lattice field models both in finite and infinite volume.
They have been applied to quantum spin models and field theories at finite
temperature. The models considered are subject to a global symmetry
or to an even larger symmetry group such as O(N) with . In this paper
we are concerned with the technical details of series computations to allow for
a nontrivial vacuum expectation value , which is typical for
models that break a global symmetry. Examples are scalar fields
coupled to an external field, or manifestly gauge invariant effective models of
Higgs field condensates in the electroweak theory, even in the high temperature
phase. A nonvanishing tadpole implies an enormous proliferation of graphs and
limits the graphical series computation to the 10th order. To achieve the
hopping parameter series to comparable order as in the symmetric
case, the graphical expansion is replaced by an expansion into new algebraic
objects called vertex structures. In this way the 18th order becomes feasible.Comment: 19 pages, latex2
Dynamical linke cluster expansions: Algorithmic aspects and applications
Dynamical linked cluster expansions are linked cluster expansions with
hopping parameter terms endowed with their own dynamics. They amount to a
generalization of series expansions from 2-point to point-link-point
interactions. We outline an associated multiple-line graph theory involving
extended notions of connectivity and indicate an algorithmic implementation of
graphs. Fields of applications are SU(N) gauge Higgs systems within variational
estimates, spin glasses and partially annealed neural networks. We present
results for the critical line in an SU(2) gauge Higgs model for the electroweak
phase transition. The results agree well with corresponding high precision
Monte Carlo results.Comment: LATTICE98(algorithms
Power-counting theorem for staggered fermions
Lattice power-counting is extended to QCD with staggered fermions. As
preparation, the difficulties encountered by Reisz's original formulation of
the lattice power-counting theorem are illustrated. One of the assumptions that
is used in his proof does not hold for staggered fermions, as was pointed out
long ago by Luscher. Finally, I generalize the power-counting theorem, and the
methods of Reisz's proof, such that the difficulties posed by staggered
fermions are overcome.Comment: 29 pages, added 2 figures, one more example, clarifying remarks and
one reference; misstatement regarding irrelevant vertices correcte
Renormalization of lattice gauge theories with massless Ginsparg Wilson fermions
Using functional techniques, we prove, to all orders of perturbation theory,
that lattice vector gauge theories with Ginsparg Wilson fermions are
renormalizable. For two or more massless fermions, they satisfy a flavour
mixing axial vector Ward identity. It involves a lattice specific part that is
quadratic in the vertex functional and classically irrelevant. We show that it
stays irrelevant under renormalization. This means that in the continuum limit
the (standard) chiral symmetry becomes restored. In particular, the flavour
mixing current does not require renormalization.Comment: 13 pages, Latex2
Lattice QED and Universality of the Axial Anomaly
We give a perturbative proof that U(1) lattice gauge theories generate the
axial anomaly in the continuum limit under very general conditions on the
lattice Dirac operator. These conditions are locality, gauge covariance and the
absense of species doubling. They hold for Wilson fermions as well as for
realizations of the Dirac operator that satisfy the Ginsparg-Wilson relation.
The proof is based on the lattice power counting theorem. The results
generalize to non-abelian gauge theories.Comment: LATTICE99(theoretical developments) 3 page
Background field technique and renormalization in lattice gauge theory
Lattice gauge theory with a background gauge field is shown to be
renormalizable to all orders of perturbation theory. No additional counterterms
are required besides those already needed in the absence of the background
field. The argument closely follows the treatment given earlier for the case of
dimensional regularization by Kluberg-Stern and Zuber. It is based on the BRS,
background gauge and shift symmetries of the lattice functional integral.Comment: 26 pages, uuencoded compressed postscript fil
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