Influence of cubic and dipolar anisotropies on the static and dynamic coexistence anomalies of the time-dependent Ginzburg-Landau models

Abstract

In isotropic systems below the transition temperature, the massless Goldstone modes imply critical infrared singularities in the statics and dynamics along the entire coexistence curve. We examine the important question whether these coexistence anomalies are of relevance also in more realistic systems displaying anisotropies. By applying a generalized renormalization scheme to the time-dependent Ginzburg-Landau models, we treat two quite different but characteristic cases, namely the influence of (i) weak cubic anisotropies, and (ii) long-range dipolar interactions. In the presence of cubic terms, the transverse excitations acquire a mass and thus one expects the theory to approach an uncritical "Gaussian" regime in the limit ${\vec q} \rightarrow 0$ and $ω\rightarrow 0$. Therefore, we first consider the one-component case in order to show that our formalism also provides a consistent description of the crossover into an asymptotically Gaussian theory. In the case of (weak) cubic anisotropies, the fact that for $n < 4$ the fluctuations tend to restore the $O(n)$-symmetry at the critical point proves to be most important, since under these circumstances coexistence-type singularities may be found in an intermediate wavenumber and frequency range. The dipolar interaction induces an anisotropy in momentum space, which does not completely destroy the massless character of the transverse fluctuations, but only effectively reduces the number of Goldstone modes by one. Remarkably, similar to the isotropic case the asymptotic theory can be treated exactly. For $n \geq 3$ we find coexistence anomalies governed by the isotropic power laws. However, the amplitudes of the respective scaling functions depend on the angle between order parameter and external wavevector.