Physical review. E, Statistical, nonlinear, andâ€¦

2009

Many physical and physiological signals exhibit complex scale-invariant features characterized by 1/f scaling and long-range power-law correlations, indicating a possibly common control mechanism.â€¦ (More)

For an anisotropic Euclidean f theory with two interactions@u(( i 51 M f i )21v( i 51 M f i # theb functions are calculated from five-loop perturbation expansions in d542Â« dimensions, using theâ€¦ (More)

For an anisotropic euclidean Ï†4-theory with two interactions [u( âˆ‘M i=1 Ï† 2 i ) 2+v âˆ‘M i=1 Ï† 4 i ] the Î²-functions are calculated from five-loop perturbation expansions in d = 4âˆ’ Îµ dimensions, usingâ€¦ (More)

Recently, one of us [1, 2] has developed a new approach to critical exponents of field theories based on the strong-coupling limit of variational perturbation expansions [3] and [4]3. This limit isâ€¦ (More)

1 Introduction Systems containing a large number of particles exhibit a great variety of phase transitions. Most common are first-and second-order transitions. A transition is said to be first-orderâ€¦ (More)

A thermally fluctuating field theory is defined by means of a functional integral representation of the partition function, in which the fields are coupled linearly to external sources. Thisâ€¦ (More)

10 Renormalization Group The renormalization procedure in the last chapter has eliminated all UV-divergences from the Feynman integrals arising from large momenta in D = 4 âˆ’ Îµ dimensions. This wasâ€¦ (More)

In Section 5.4, we have developed a functional formalism to find all connected vacuum diagrams and their multiplicities. These serve as a basis for deriving all diagrams contributing to twoandâ€¦ (More)

A powerful and yet mathematically simple method of resumming divergent perturbation expansions for critical exponents is provided by variational perturbation theory. This is a systematic extension ofâ€¦ (More)

Massive Feynman integrals containing more than one loop momentum are hard to evaluate. Fortunately, the understanding of the critical behavior of the field theory requires only knowledge of theâ€¦ (More)