Critical dynamics below T_c

Abstract

Going below the critical temperature, the existence of a non-zero average value of the order parameter induces qualitatively new features in the critical behaviour in a variety of systems. A crucial role is played by the symmetry in the intrinsic space of the order parameter degrees of freedom. This lecture is focused on rotationally invariant systems, others are only briefly mentioned.

At first, properties of the isotropic multicomponent systems are described on a phenomenological basis in cases of purely dissipative systems and of systems with reversible mode coupling as well. The main feature is that the orientational fluctuations are dominating the large-distance, long-time behaviour of the system, and the parallel and longitudinal order parameter correlation functions can be expressed in terms of the correlation function for the orientational fluctuations. In the purely relaxational model such qualitative arguments predict a power-law decay in space and time of the correlation functions.

These properties are subsequently considered within the framework of the semimacroscopic theory. In this context the theoretical means to handle the problems in the ordered phase i.e. new type of building blocks replacing the usual self energies are introduced, both for the transverse and longitudinal order parameter response and correlation functions. It is shown how characteristics of the Goldstone mode can be expressed in terms of them. The longitudinal correlation function is discussed especially from the point of view of how the results of the phenomenological considerations can be justified.

Special emphasis is given to purely dynamic effects, such as the Goldstone-mode induced singularity in the transport coefficient of the parallel total magnetization in an isotropic antiferromagnet, recently investigated also experimentally. It is shown that the theory can account for the experimental findings in RbMnr3 , not only concerning the wave-number dependence of the transport coefficient in the hydrodynamic region but also regarding its magnitude.