2,640 research outputs found
Equivalent Fixed-Points in the Effective Average Action Formalism
Starting from a modified version of Polchinski's equation, Morris'
fixed-point equation for the effective average action is derived. Since an
expression for the line of equivalent fixed-points associated with every
critical fixed-point is known in the former case, this link allows us to find,
for the first time, the analogous expression in the latter case.Comment: 30 pages; v2: 29 pages - major improvements to section 3; v3:
published in J. Phys. A - minor change
Sensitivity of Nonrenormalizable Trajectories to the Bare Scale
Working in scalar field theory, we consider RG trajectories which correspond
to nonrenormalizable theories, in the Wilsonian sense. An interesting question
to ask of such trajectories is, given some fixed starting point in parameter
space, how the effective action at the effective scale, Lambda, changes as the
bare scale (and hence the duration of the flow down to Lambda) is changed. When
the effective action satisfies Polchinski's version of the Exact
Renormalization Group equation, we prove, directly from the path integral, that
the dependence of the effective action on the bare scale, keeping the
interaction part of the bare action fixed, is given by an equation of the same
form as the Polchinski equation but with a kernel of the opposite sign. We then
investigate whether similar equations exist for various generalizations of the
Polchinski equation. Using nonperturbative, diagrammatic arguments we find that
an action can always be constructed which satisfies the Polchinski-like
equation under variation of the bare scale. For the family of flow equations in
which the field is renormalized, but the blocking functional is the simplest
allowed, this action is essentially identified with the effective action at
Lambda = 0. This does not seem to hold for more elaborate generalizations.Comment: v1: 23 pages, 5 figures, v2: intro extended, refs added, published in
jphy
Strain control of superlattice implies weak charge-lattice coupling in LaCaMnO
We have recently argued that manganites do not possess stripes of charge
order, implying that the electron-lattice coupling is weak [Phys Rev Lett
\textbf{94} (2005) 097202]. Here we independently argue the same conclusion
based on transmission electron microscopy measurements of a nanopatterned
epitaxial film of LaCaMnO. In strain relaxed regions, the
superlattice period is modified by 2-3% with respect to the parent lattice,
suggesting that the two are not strongly tied.Comment: 4 pages, 4 figures It is now explained why the work provides evidence
to support weak-coupling, and rule out charge orde
On the Renormalization of Theories of a Scalar Chiral Superfield
An exact renormalization group for theories of a scalar chiral superfield is
formulated, directly in four dimensional Euclidean space. By constructing a
projector which isolates the superpotential from the full Wilsonian effective
action, it is shown that the nonperturbative nonrenormalization theorem
follows, quite simply, from the flow equation. Next, it is argued that there do
not exist any physically acceptable non-trivial fixed points. Finally, the
Wess-Zumino model is considered, as a low energy effective theory. Following an
evaluation of the one and two loop beta-function coefficients, to illustrate
the ease of use of the formalism, it is shown that the beta-function in the
massless case does not receive any nonperturbative power corrections.Comment: 52 pages, 4 figures; v2: 57 pages - refs added and some minor
corrections/clarifications made; v3: published in JHEP - some further
clarifications mad
Chiral phase boundary of QCD at finite temperature
We analyze the approach to chiral symmetry breaking in QCD at finite
temperature, using the functional renormalization group. We compute the running
gauge coupling in QCD for all temperatures and scales within a simple truncated
renormalization flow. At finite temperature, the coupling is governed by a
fixed point of the 3-dimensional theory for scales smaller than the
corresponding temperature. Chiral symmetry breaking is approached if the
running coupling drives the quark sector to criticality. We quantitatively
determine the phase boundary in the plane of temperature and number of flavors
and find good agreement with lattice results. As a generic and testable
prediction, we observe that our underlying IR fixed-point scenario leaves its
imprint in the shape of the phase boundary near the critical flavor number:
here, the scaling of the critical temperature is determined by the
zero-temperature IR critical exponent of the running coupling.Comment: 39 pages, 8 figure
Functional renormalization group with a compactly supported smooth regulator function
The functional renormalization group equation with a compactly supported
smooth (CSS) regulator function is considered. It is demonstrated that in an
appropriate limit the CSS regulator recovers the optimized one and it has
derivatives of all orders. The more generalized form of the CSS regulator is
shown to reduce to all major type of regulator functions (exponential,
power-law) in appropriate limits. The CSS regulator function is tested by
studying the critical behavior of the bosonized two-dimensional quantum
electrodynamics in the local potential approximation and the sine-Gordon scalar
theory for d<2 dimensions beyond the local potential approximation. It is shown
that a similar smoothing problem in nuclear physics has already been solved by
introducing the so called Salamon-Vertse potential which can be related to the
CSS regulator.Comment: JHEP style, 11 pages, 2 figures, proofs corrected, accepted for
publication by JHE
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