Relationship between Fujikawa's Method and the Background Field Method for the Scale Anomaly

We show the equivalence between Fujikawa's method for calculating the scale anomaly and the diagrammatic approach to calculating the effective potential via the background field method, for an $O(N)$ symmetric scalar field theory. Fujikawa's method leads to a sum of terms, each one superficially in one-to-one correspondence with a vacuum diagram of the 1-loop expansion. From the viewpoint of the classical action, the anomaly results in a breakdown of the Ward identities due to a scale-dependence of the couplings, whereas in terms of the effective action, the anomaly is the result of the breakdown of Noether's theorem due to explicit symmetry breaking terms of the effective potential.Comment: 9 pages (this version is the published version

Effect of temperature-dependent shape anisotropy on coercivity with aligned Stoner-Wohlfarth soft ferromagnets

The temperature variation effect of shape anisotropy on the coercivity, HC(T), for the aligned Stoner-Wohlfarth (SW) soft ferromagnets, such as fcc Ni, fcc Co and bcc Fe, are investigated within the framework of Neel-Brown (N-B) analysis. An extended N-B equation is thus proposed,by introducing a single dimensionless correction function, the reduced magnetization, m(\tao) = MS(T)/MS(0), in which \tao = T/TC is the reduced temperature, MS(T) is the saturation magnetization, and TC is the Curie temperature. The factor, m(\tao), accounts for the temperature-dependent effect of the shape anisotropy. The constants, H0 and E0, are for the switching field at zero temperature and the potential barrier at zero field, respectively. According to this newly derived equation, the blocking temperature above which the properties of superparamagnetism show up is described by the expression, TB = E0m^2(\tao)/[kBln(t/t0)], with the extra correction factor m^2(\tao). The possible effect on HC(T) and the blocking temperature, TB, attributed to the downshift of TC resulting from the finite size effect has been discussed also.Comment: 22 pages, 2 figures, 1 table, Accepted by Phys. Rev.

Quantitative comparisons of type 3 radio burst intensity and fast electron flux at 1 AU

The flux of fast solar electrons and the intensity of the type 111 radio emission generated by these particles were compared at one AU. Two regimes were found in the generation of type 111 radiation: one where the radio intensity is linearly proportional to the electron flux, and another, which occurs above a threshold electron flux, where the radio intensity is approximately proportional to the 2.4 power of the electron flux. This threshold appears to reflect a transition to a different emission mechanism