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Two-loop Feynman integrals of the massive $phi^4_d$ field theory are explicitly obtained for generic space dimensions $d$. Corresponding renormalization-group functions are expressed in a compact form in terms of Gauss hypergeometric functions. A number of interesting and useful relations is given for these integrals as well as for several special mathematical functions and constants.
Critical two-point correlation functions in the continuous and lattice phi^4 models with scalar order parameter phi are considered. We show by different non-perturbative methods that the critical correlation functions <phi^n(0) phi^m(x)> are proporti
We derive exact analytic results for several four-point correlation functions for statistical models exhibiting phase separation in two-dimensions. Our theoretical results are then specialized to the Ising model on the two-dimensional strip and found
We determine universal critical exponents that describe the continuous phase transitions in different dimensions of space. We use continued functions without any external unknown parameters to obtain analytic continuation for the recently derived 7-
We show that the exact beta-function beta(g) in the continuous 2D gPhi^{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 approximate val
We provide an analysis of the structure of renormalisation scheme invariants for the case of $phi^4$ theory, relevant in four dimensions. We give a complete discussion of the invariants up to four loops and include some partial results at five loops,