Variational perturbation theory
- Variational perturbation theory
In mathematics, variational perturbation theory is a mathematical method to convert divergent power series in a small expansion parameter, say
:,
into a convergent series in powers
:,
where is a critical exponent. This is possible with the help of variational parameters, which are determined by optimization order by order in .
Variational perturbation theory is an important mathematical tool in the theory of critical phenomena. It has led to the most accurate predictions of critical exponents.
See also
* Variational method (quantum mechanics)
References
* Hagen Kleinert, "Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets", 3. Auflage, [http://www.worldscibooks.com/physics/5057.html World Scientific (Singapore, 2004)] (readable online [http://www.physik.fu-berlin.de/~kleinert/b5 here] )" (see Chapter 15)
* Hagen Kleinert and Verena Schulte-Frohlinde, "Critical Properties of φ4-Theories", [http://www.worldscibooks.com/physics/4733.html World Scientific (Singapur, 2001)] ; Paperback ISBN 981-02-4658-7 "(readable online [http://www.physik.fu-berlin.de/~kleinert/b8 here] )" (see Chapter 19)
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