Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-05-30
Phys.Lett. B334 (1994) 355-362
Physics
High Energy Physics
High Energy Physics - Theory
15 pages (with figures), Plain TeX, uses psfig, 5 postscript figures appended as uuencoded compressed tar file, SHEP 93/94-23,
Scientific paper
10.1016/0370-2693(94)90700-5
We investigate the Exact Renormalization Group (ERG) description of ($Z_2$ invariant) one-component scalar field theory, in the approximation in which all momentum dependence is discarded in the effective vertices. In this context we show how one can perform a systematic search for non-perturbative continuum limits without making any assumption about the form of the lagrangian. Concentrating on the non-perturbative three dimensional Wilson fixed point, we then show that the sequence of truncations $n=2,3,\dots$, obtained by expanding about the field $\varphi=0$ and discarding all powers $\varphi^{2n+2}$ and higher, yields solutions that at first converge to the answer obtained without truncation, but then cease to further converge beyond a certain point. No completely reliable method exists to reject the many spurious solutions that are also found. These properties are explained in terms of the analytic behaviour of the untruncated solutions -- which we describe in some detail.
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