Field theory of bicritical and tetracritical points. III. Relaxational dynamics including conservation of magnetization (Model C)

TL;DR

This paper investigates the relaxational dynamical critical behavior of systems with combined symmetries, including magnetization conservation, using two-loop RG theory, revealing strong dynamical scaling and nonuniversal transient effects.

Contribution

It extends the understanding of dynamical critical behavior in systems with $O(n_ ext{||}) imes O(n_ot)$ symmetry, incorporating conservation laws via two-loop RG calculations.

Findings

Strong dynamical scaling with $z=2rac{}{ u}-1$ in certain fixed points.

Presence of a small transient exponent at specific symmetry values leading to nonuniversal behavior.

Temperature dependence of magnetic transport coefficients shows nonasymptotic effects.

Abstract

We calculate the relaxational dynamical critical behavior of systems of $O(n_\|)\oplus O(n_\perp)$ symmetry including conservation of magnetization by renormalization group (RG) theory within the minimal subtraction scheme in two loop order. Within the stability region of the Heisenberg fixed point and the biconical fixed point strong dynamical scaling holds with the asymptotic dynamical critical exponent $z=2\phi/\nu-1$ where $\phi$ is the crossover exponent and $\nu$ the exponent of the correlation length. The critical dynamics at $n_\|=1$ and $n_\perp=2$ is governed by a small dynamical transient exponent leading to nonuniversal nonasymptotic dynamical behavior. This may be seen e.g. in the temperature dependence of the magnetic transport coefficients.