相关论文: Renormalization Group Functions of the \phi^4 Theo…
Reconstruction of the \beta-function for \phi^4 theory, attempted previously by summation of perturbation series, leads to asymptotics \beta(g)=\beta_\infty g^\alpha at g\to\infty, where \alpha\approx 1 for space dimensions d=2,3,4. The…
The previously obtained analytical asymptotic expressions for the Gell-Mann - Low function \beta(g) and anomalous dimensions of \phi^4 theory in the limit g\to\infty are based on the parametric representation of the form g = f(t), \beta(g)…
Summation of the perturbation series for the Gell-Mann--Low function \beta(g) of \phi^4 theory leads to the asymptotics \beta(g)=\beta_\infty g^\alpha at g\to\infty, where \alpha\approx 1 for space dimensions d=2,3,4. The natural hypothesis…
The well-known algorithm for summing of divergent series is based on the Borel transformation in combination with the conformal mapping (Le Guillou and Zinn-Justin, 1977). Modification of this algorithm allows to determine a strong coupling…
An algorithm is proposed for the determination of the asymptotics of a sum of a perturbation series from the given values of its coefficients in the strong-coupling limit. When applied to the \Phi^4 theory, the algorithm yields the…
An algorithm is proposed for determining asymptotics of the sum of a perturbative series in the strong coupling limit using given values of the expansion coefficients. Operation of the algorithm is illustrated by test examples, method for…
It has been previously shown that calculation of renormalization group (RG) functions of the scalar \phi^4 theory reduces to the analysis of thermodynamic properties of the Ising model. Using high-temperature expansions for the latter, RG…
We discuss the analytic properties of the Callan-Symanzik beta-function beta(g) associated with the zero-momentum four-point coupling g in the two-dimensional phi^4 model with O(N) symmetry. Using renormalization-group arguments, we derive…
According to recent results, the Gell-Mann - Low function \beta(g) of four-dimensional \phi^4 theory is non-alternating and has a linear asymptotics at infinity. According to the Bogoliubov and Shirkov classification, it means possibility…
The presence or absense of renormalon singularities in the Borel plane is shown to be determined by the analytic properties of the Gell-Mann - Low function \beta(g) and some other functions. A constructive criterion for the absense of…
The critical behaviour of a non-local scalar field theory is studied. This theory has a non-local kinetic term which involves a real power 1-2\alpha of the Laplacian. The interaction term is the usual local \phi^{4} interaction. The lowest…
We compute the one-loop \beta-functions describing the renormalisation of the coupling constant \lambda and the frequency parameter \Omega for the real four-dimensional duality-covariant noncommutative \phi^4-model, which is renormalisable…
We investigate possible renormalization-group fixed points at nonzero coupling in $\phi^3$ theories in six spacetime dimensions, using beta functions calculated to the four-loop level. We analyze three theories of this type, with (a) a…
We show that the exact beta-function \beta(g) in the continuous 2D g\Phi^{4} model possesses the Kramers-Wannier duality symmetry. The duality symmetry transformation \tilde{g}=d(g) such that \beta(d(g))=d'(g)\beta(g) is constructed and the…
We derive the Gell-Mann and Low renormalization group equation in the Wilsonian approach to renormalization of massless $g\phi^4$ in four dimensions, as a particular case of a non-linear equation satisfied at any scale by the Wilsonian…
This is a lecture note on the renormalization group theory for field theory models based on the dimensional regularization method. We discuss the renormalization group approach to fundamental field theoretic models in low dimensions. We…
We study the renormalization group flow in a class of scalar-tensor theories involving at most two derivatives of the fields. We show in general that minimal coupling is self consistent, in the sense that when the scalar self couplings are…
Within the context of massive N-component $\phi^4$ scalar field theory, we use asymptotic Pade-approximant methods to estimate from prior orders of perturbation theory the five-loop contributions to the coupling-constant beta-function…
The renormalization-group functions of the two-dimensional n-vector \lambda \phi^4 model are calculated in the five-loop approximation. Perturbative series for the \beta-function and critical exponents are resummed by the Pade-Borel-Leroy…
We present a renormalization group analysis for the hyperbolic sine-Gordon (sinh-Gordon) model in two dimensions. We derive the renormalization group equations based on the dimensional regularization method and the Wilson method. The same…