Longitudinal and transverse Greens functions in phi^4 model below and near the critical point

dc.creatorKaupuzs, J.
dc.date2002-02-25
dc.date2004-06-29
dc.date.accessioned2026-07-07T02:44:31Z
dc.date.available2026-07-07T02:44:31Z
dc.descriptionWe have extended our method of grouping of Feynman diagrams (GFD theory) to study the transverse (G_t) and longitudinal (G_l) Greens functions in phi^4 model below the critical point (T<T_c) 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<T_c and T>T_c. The long-wave limit k->0 has been studied at T<T_c, showing that the transverse and the longitudinal correlation functions diverge as 1/k in the power of lambda_t and lambda_l, respectively, where d/2< lambda_t < 2 and lambda_l = 2 lambda_t - 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 -> T_c 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 bM^2/a^2 (where M is magnetization, a and b are the amplitudes of G_t and G_l at k->0) are universal. The results of the perturbative RG method are reproduced by formally setting lambda_t=2. Nevertheless, we disprove the conventional statement that lambda_t=2 is the exact result.
dc.descriptionThe 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
dc.identifierhttps://arxiv.org/abs/cond-mat/0202416
dc.identifierhttp://arxiv.org/abs/cond-mat/0202416
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/18953
dc.subjectStatistical Mechanics
dc.titleLongitudinal and transverse Greens functions in phi^4 model below and near the critical point
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