Dynamics of the ferromagnet in 2 + ε dimensions

Erwin Frey, Franz Schwabl

Kyozi Kawasaki

A renormalization group equation for the inverse propagator is obtained for a stochastic model of isotropic Heisenberg ferromagnet, whose solution at a fixed point yields the dynamical scaling law with the correct dynamic critical exponent. For 6-ε dimensions (ε>0) we describe an iterative method to obtain an ε-expansion for the inverse propagator.

Sergei V. Maleev

Shang-keng Ma, Gene F. Mazenko

The critical dynamics of a model isotropic ferromagnet is studied in $6\ensuremath{-}\ensuremath{\epsilon}$ dimensions both above and below ${T}_{c}$. The renormalization group and the characteristic frequency exponent $z$ are determined to order $\ensuremath{\epsilon}$. Implications of the renormalization group are discussed. A direct calculation of the dynamic response function to order $\ensuremath{\epsilon}$ shows many interesting features, especially for $T<{T}_{c}$.

Kun Yang

We use bosonization to derive the effective field theory that properly describes ferromagnetic transition in one-dimensional itinerant electron systems. The resultant theory is shown to have dynamical exponent z = 2 at tree level and upper critical dimension dc = 2. Thus one dimension is below the upper critical dimension of the theory, and the critical behavior of the transition is controlled by an interacting fixed point, which we study via epsilon expansion. Comparisons will be made with the Hertz-Millis theory, which describes the ferromagnetic transition in higher dimensions.

George Allen Baker Jr., H.E. Gilbert, Jemimah K. Eve +1 more