Tricritical Dynamics at the Demixing-λ-Transition in 3He-4He Mixtures

Abstract

We calculate in two loop order the dynamical critical behavior at the tricritical point occuring in 3He-4He mixtures. Model F′ introduced by Siggia and Nelson (Phys. Rev. B 15:1427, [1977])—already problematic in one loop order—is shown in two loop order to lead to a divergence of the mass diffusion D in contradiction to experiments. Within the complex symmetric version of this model (model E⋆′) the dynamical critical exponents of the kinetic coefficients can be calculated exactly leading to a mass diffusion going to zero at the tricritical point as D(tX)∼tX1/2 (tX is the relative temperature distance at constant concentration) and the thermal diffusion ratio kT∼tX−1 diverges proportional to the concentration susceptibility in the experimental region. We also discuss effective dynamical critical exponents and compare them with recent simulations of the vector Blume-Emery-Griffths model.