Field-Theoretic Variational Perturbation Theory
 
This theory allows for the arbitrarily precise calculations of strong-coupling properties
of quantum field theories. In particular, it enables one to find critical exponents
near second-order phase transitions in a simple way
without using renormalization group theory.
It makes essential use of the Wegner exponent
governing the approach to scaling
(which Pade and Pade-Borel methods are unable to do)
and determines it with high accuracy. The theory is based on an essential extension of the original
Feynman-Kleinert Variational Approach
in two steps.
 
First, the Peierls inequality was abandoned in order to
deal with expansions of any order. This turns divergent weak-coupling expansions
into convergent strong-coupling expansions.  The convergence is mostly exponentially fast.
The details are described in Chapter 5 of my textbook
 
Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets
 
Second, a simple trick was found to accommodate
the anomalous dimensions of quantum field theory. The result is

Field-Theoretic Variational Perturbation Theory
which has led to the most reliable results of strong-coupling
properties of field theories so far.
The most-accurately measured strong-coupling property is the critical exponent
that governs the singularity of the specific heat of superfluid helium,
which was performed with great effort in amicrogravity environment
in a satellite by J. Lipa and collaborators. This experiment
found precisely the value which I predicted in a seven-loop calculation. For details, see
my  textbook on this subject

Critical Properties of phi^4 Theories.


The relevant papers are