Most Accurate Critical Exponents

H. Kleinert, "Seven Loop Critical Exponents from Strong-Coupling $\phi^4$-Theory in Three Dimensions"

Predicts the critical exponent alpha governing the peak in the specific heat
of superfluid helium at the lambda transition alpha = -- 0.0129.
The recent famous satellite experiment by

J. A. Lipa, J. A. Nissen, D. A. Stricker, D. R. Swanson, T. C. P. Chui
Specific Heat of Liquid Helium in Zero Gravity very near the Lambda Point
, publ. in Phys. Rev. B 68, 174518 (2003)

found same value alpha = -- 0.0127.

Subject is reviewed here:
M. Barmatz, Inseob Hahn, J.A. Lipa, and R.V. Duncan, Rev. Mod. Phys. 79, 1 (2007)
Critical phenomena in microgravity: Past, present, and future

See also Kleinert's related papers:

Strong-Coupling Behavior of Phi^4-Theories and Critical Exponents
Critical Exponents without beta-Function

Variational Resummation of $\epsilon$-Expansions of Critical Exponents
of Nonlinear O($N$)-Symmetric $\sigma$-Model in $2+ \epsilon$ Dimensions

Strong-Coupling $\phi^4$-Theory in $4- \epsilon$ Dimensions, and Critical Exponents

Everything is contained in the textbook on critical phenomena

H Kleinert and V Schulte-Frohlinde
Critical Properties of Phi^4 Theories
World Scientific, Singapore, 2001
(Hardcover ISBN 981-02-4658-7 US$46, Paperback ISBN 981-02-4659-5 US$22, Click here to order!)

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