and critical exponents

With the help of variational perturbation theory we continue the renormalization constants of f 4-theories in 4ye dimensions to infinitely strong bare couplings g and find their power behavior in g, thereby determining all critical0 0 exponents without the standard renormalization group techniques. q 1998 Published by Elsevier Science B.V. All rights reserved. w x1. In a recent paper 1 we have shown that there exists a simple way of extracting the strong-coupling properties of a f 4-theory from perturbation expan-sions. In particular, we were able to find the power behavior of the renormalization constants in the limit of large couplings, and from this all critical expo-nents of the system. By using the known expansion coefficients of the renormalization constants in three dimensions up to six loops we derived extremely accurate values for the critical exponents. The method is a systematic extension of the Feynman-Kleinert w xvariational approximation to path integrals 2 to w xarbitrary orders 3. For an anharmonic oscillator, the derived variational perturbation expansions converge uniformly and exponentially fast, like eyconst=N 1r3 in w xthe order N of the approximation 4,5. The same type of convergence seems to exist also for the 1 E-mail: kleinert @ physik.fu-berlin.de