The dynamic critical exponents of classical liquids are studied on the basis of the mode coupling theory. The shear viscosity for the spatial dimensionality between two and four exhibits the weak power law divergence at a critical point, which was briefly reported in a previous paper. The non-Markoffian effects and the vertex corrections are also investigated. It is shown that both corrections have only small contributions to the order parameter decay rate and do not affect the dynamic critical exponents.The dynamic critical exponents of classical liquids are studied on the basis of the mode coupling theory. The shear viscosity for the spatial dimensionality between two and four exhibits the weak power law divergence at a critical point, which was briefly reported in a previous paper. The non-Markoffian effects and the vertex corrections are also investigated. It is shown that both corrections have only small contributions to the order parameter decay rate and do not affect the dynamic critical exponents.

Progress of Theoretical PhysicsMay 1, 197686 citations

Scaling Laws for Dynamic Critical Phenomena

Wilhelm Brenig

Springer eBooksJan 1, 19890 citations

Theory of dynamic critical phenomena

Pierre C. Hohenberg, Bertrand I. Halperin

An introductory review of the central ideas in the modern theory of dynamic critical phenomena is followed by a more detailed account of recent developments in the field. The concepts of the conventional theory, mode-coupling, scaling, universality, and the renormalization group are introduced and are illustrated in the context of a simple example---the phase separation of a symmetric binary fluid. The renormalization group is then developed in some detail, and applied to a variety of systems. The main dynamic universality classes are identified and characterized. It is found that the mode-coupling and renormalization group theories successfully explain available experimental data at the critical point of pure fluids, and binary mixtures, and at many magnetic phase transitions, but that a number of discrepancies exist with data at the superfluid transition of $^{4}\mathrm{He}$ .An introductory review of the central ideas in the modern theory of dynamic critical phenomena is followed by a more detailed account of recent developments in the field. The concepts of the conventional theory, mode-coupling, scaling, universality, and the renormalization group are introduced and are illustrated in the context of a simple example---the phase separation of a symmetric binary fluid. The renormalization group is then developed in some detail, and applied to a variety of systems. The main dynamic universality classes are identified and characterized. It is found that the mode-coupling and renormalization group theories successfully explain available experimental data at the critical point of pure fluids, and binary mixtures, and at many magnetic phase transitions, but that a number of discrepancies exist with data at the superfluid transition of $^{4}\mathrm{He}$.

Reviews of Modern PhysicsJul 1, 19776,905 citations

Dynamical Critical Phenomena and Related Topics

Charles Paul Enz

Lecture notes in physicsJan 1, 1979196 citations

Renormalization-group and mode-coupling theories of critical dynamics

Kyozi Kawasaki, J. D. Gunton

We discuss renormalization-group and mode-coupling theories of critical dynamics for several models. We show that to lowest order in $\ensuremath{\epsilon}={d}_{c}\ensuremath{-}d$, where for $d>{d}_{c}$ conventional theory is valid, the renormalizationgroup differential equations are related by a simple transformation to those obtained from mode-coupling theory. Furthermore, the values of the dynamical fixed-point parameters essentially coincide with the critical amplitudes of the diverging transport coefficients, as determined by mode-coupling theory. In addition, we present a correct renormalization-group treatment for dynamical systems with more than one time scale, as for the binary liquid. We stress the fact that there are two distinct classes of critical dynamics, as illustrated by the results for the models studied here. We also discuss the instability of the conventional fixed point (time-dependent Ginzburg-Landau like) against mode-coupling perturbations for $d<{d}_{c}$ , with particular emphasis on a model for superfluid helium.We discuss renormalization-group and mode-coupling theories of critical dynamics for several models. We show that to lowest order in $\ensuremath{\epsilon}={d}_{c}\ensuremath{-}d$, where for $d>{d}_{c}$ conventional theory is valid, the renormalizationgroup differential equations are related by a simple transformation to those obtained from mode-coupling theory. Furthermore, the values of the dynamical fixed-point parameters essentially coincide with the critical amplitudes of the diverging transport coefficients, as determined by mode-coupling theory. In addition, we present a correct renormalization-group treatment for dynamical systems with more than one time scale, as for the binary liquid. We stress the fact that there are two distinct classes of critical dynamics, as illustrated by the results for the models studied here. We also discuss the instability of the conventional fixed point (time-dependent Ginzburg-Landau like) against mode-coupling perturbations for $d<{d}_{c}$, with particular emphasis on a model for superfluid helium.

Physical review. B, Solid stateJun 1, 197651 citations

^{4}\mathrm{He}

We discuss renormalization-group and mode-coupling theories of critical dynamics for several models. We show that to lowest order in $\ensuremath{\epsilon}={d}_{c}\ensuremath{-}d$, where for

d>{d}_{c}

conventional theory is valid, the renormalizationgroup differential equations are related by a simple transformation to those obtained from mode-coupling theory. Furthermore, the values of the dynamical fixed-point parameters essentially coincide with the critical amplitudes of the diverging transport coefficients, as determined by mode-coupling theory. In addition, we present a correct renormalization-group treatment for dynamical systems with more than one time scale, as for the binary liquid. We stress the fact that there are two distinct classes of critical dynamics, as illustrated by the results for the models studied here. We also discuss the instability of the conventional fixed point (time-dependent Ginzburg-Landau like) against mode-coupling perturbations for

d<{d}_{c}

, with particular emphasis on a model for superfluid helium.