Browsing by Author "Stancu, Ion"

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    Second-order corrections to the Gaussian effective potential for lambda phi(4) and other theories
    (1990) Stancu, Ion; Stevenson, Paul M.
    We formulate a systematic, nonperturbative expansion for the effective potential of $\lambda\phi\sp4$ theory. At first order it gives the Gaussian effective potential (GEP), which itself contains the 1-loop and leading-order $1\over N$ results. Here, we compute the second-order terms and hence obtain the post-Gaussian effective potential (PGEP) in 1, 2, 3, and 4 spacetime dimensions. The renormalization procedure, including the calculation of the physical mass, is discussed in detail. The results in lower dimensions agree well with the GEP when the comparison is made for the same values of the bare parameters. In 4 dimensions the divergent integrals are calculated using coordinate-space methods combined with dimensional regularization. (Difficulties with other regularizations are briefly discussed). The PGEP for the "precarious" $\lambda\phi\sp4$ theory is obtained in manifestly finite form. Remarkably, the final result takes the same mathematical form as the GEP, with only some numerical co-efficients being changed. Indeed, when parametrized in terms of the physical mass and the renormalized coupling constant, only a single coefficient is changed, from 1 to 1-1/(N + 3)$\sp2$. The "autonomous" version of the 4-dimensional theory refuses to work in this approach: one obtains indeed an autonomous-like theory, but it is unbounded below for a certain range of the parameters. The influence of fermions on scalar systems is also investigated in the post-Gaussian approximation. For the simple case of an Yukawa-type coupling with no scalar self-interaction terms the results turn out to be the same as in the Gaussian approximation.
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    The isotropic N-vector model in random magnetic fields
    (1988) Stancu, Ion; Stevenson, Paul M.
    We have investigated the dynamics of the isotropic N-vector model with long-range exchange couplings in random magnetic fields using a 1/N expansion. The leading order is exactly solved, showing the existence of a ferromagnetic phase separated from the disordered paramagnetic phase by a line. The critical behaviour of the system has been examined in the next-to-leading order of the 1/N expansion, showing that the critical exponents are by no means related to the ones of the pure system in d-2 dimensions. The ordered phase has been also investigated in the next-to-leading order, revealing a typical Goldstone behaviour of the non time-persistent part of the transverse fluctuations. For the longitudinal fluctuations, two different types of coexistence singularities emerge, one from the non time-persistent (as in the pure systems), vanishing with the temperature, and a more divergent one from the time-persistent part of the correlation.