2002/02/25 by J. Kaupuzs, Kaupuzs, J.
Physics and Astronomy · #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/0202416
The paper has been completed by a wider discussion of literature (Sec.9.1), as well as by Monte Carlo simulations (Sec.10). Now are 32 pages and 2 figures
arxiv created 2004/06/29 · arxiv updated 2009/11/30
We have extended our method of grouping of Feynman diagrams (GFD theory) to study the transverse (Gt) and longitudinal (Gl) Greens functions in phi4 model below the critical point (T<Tc) in presence of an infinitesimal external field. Our method allows a qualitative analysis not cutting the perturbation series. We have shown that the critical behavior of the Greens (correlation) functions is consistent with a general scaling hypothesis, where the same critical exponents, found within the GFD theory, are valid both at T<Tc and T>Tc. The long-wave limit k->0 has been studied at T<Tc, showing that the transverse and the longitudinal correlation functions diverge as 1/k in the power of lambdat and lambdal, respectively, where d/2< lambdat < 2 and lambdal = 2 lambdat - d holds at the spatial dimensionality 2<d<4. It is the physical solution of our equations, which coincides with the asymptotic solution at T -> Tc as well as with a non-perturbative renormalization group (RG) analysis provided in our paper. It is confirmed also by Monte Carlo simulation. The exponents, as well as the ratio bM2/a2 (where M is magnetization, a and b are the amplitudes of Gt and Gl at k->0) are universal. The results of the perturbative RG method are reproduced by formally setting lambdat=2. Nevertheless, we disprove the conventional statement that lambdat=2 is the exact result.