114 research outputs found
Heusler-based synthetic antiferrimagnets
Antiferromagnet spintronic devices eliminate or mitigate long-range dipolar fields, thereby promising ultrafast operation. For spin transport electronics, one of the most successful strategies is the creation of metallic synthetic antiferromagnets, which, to date, have largely been formed from transition metals and their alloys. Here, we show that synthetic antiferrimagnetic sandwiches can be formed using exchange coupling spacer layers composed of atomically ordered RuAl layers and ultrathin, perpendicularly magnetized, tetragonal ferrimagnetic Heusler layers. Chemically ordered RuAl layers can both be grown on top of a Heusler layer and allow for the growth of ordered Heusler layers deposited on top of it that are as thin as one unit cell. The RuAl spacer layer gives rise to a thickness-dependent oscillatory interlayer coupling with an oscillation period of ~1.1 nm. The observation of ultrathin ordered synthetic antiferrimagnets substantially expands the family of synthetic antiferromagnets and magnetic compounds for spintronic technologies
High orders of perturbation theory: are renormalons significant?
According to Lipatov, the high orders of perturbation theory are determined
by saddle-point configurations (instantons) of the corresponding functional
integrals. According to t'Hooft, some individual large diagrams, renormalons,
are also significant and they are not contained in the Lipatov contribution.
The history of the conception of renormalons is presented, and the arguments in
favor of and against their significance are discussed. The analytic properties
of the Borel transforms of functional integrals, Green functions, vertex parts,
and scaling functions are investigated in the case of \phi^4 theory. Their
analyticity in a complex plane with a cut from the first instanton singularity
to infinity (the Le Guillou - Zinn-Justin hypothesis) is proved. It rules out
the existence of the renormalon singularities pointed out by t'Hooft and
demonstrates the nonconstructiveness of the conception of renormalons as a
whole. The results can be interpreted as an indication of the internal
consistency of \phi^4 theory.Comment: 28 pages, 8 figures include
Summing Divergent Perturbative Series in a Strong Coupling Limit. The Gell-Mann - Low Function of the \phi^4 Theory
An algorithm is proposed for determining asymptotics of the sum of a
perturbative series in the strong coupling limit using given values of the
expansion coefficients. Operation of the algorithm is illustrated by test
examples, method for estimating errors is developed, and an optimization
procedure is described. Application of the algorithm to the theory
gives a behavior at large for its Gell-Mann
-- Low function. The fact that the exponent is close to unity can be
interpreted as a manifestation of the logarithmic branching of the type
(with ), which is
confirmed by independent evidence. In any case, the theory is
internally consistent. The procedure of summing perturbartive series with
arbitrary values of expansion parameter is discussed.Comment: 23 pages, PD
Divergent Perturbation Series
Various perturbation series are factorially divergent. The behavior of their
high-order terms can be found by Lipatov's method, according to which they are
determined by the saddle-point configurations (instantons) of appropriate
functional integrals. When the Lipatov asymptotics is known and several lowest
order terms of the perturbation series are found by direct calculation of
diagrams, one can gain insight into the behavior of the remaining terms of the
series. Summing it, one can solve (in a certain approximation) various
strong-coupling problems. This approach is demonstrated by determining the
Gell-Mann - Low functions in \phi^4 theory, QED, and QCD for arbitrary coupling
constants. An overview of the mathematical theory of divergent series is
presented, and interpretation of perturbation series is discussed. Explicit
derivations of the Lipatov asymptotic forms are presented for some basic
problems in theoretical physics. A solution is proposed to the problem of
renormalon contributions, which hampered progress in this field in the late
1970s. Practical schemes for summation of perturbation series are described for
a coupling constant of order unity and in the strong-coupling limit. An
interpretation of the Borel integral is given for 'non-Borel-summable' series.
High-order corrections to the Lipatov asymptotics are discussed.Comment: Review article, 45 pages, PD
A New Approach to Solve the Low-lying States of the Schroedinger Equation
We review a new iterative procedure to solve the low-lying states of the
Schroedinger equation, done in collaboration with Richard Friedberg. For the
groundstate energy, the order iterative energy is bounded by a finite
limit, independent of ; thereby it avoids some of the inherent difficulties
faced by the usual perturbative series expansions. For a fairly large class of
problems, this new procedure can be proved to give convergent iterative
solutions. These convergent solutions include the long standing difficult
problem of a quartic potential with either symmetric or asymmetric minima.Comment: 54 pages, 3 figures given separatel
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