ABSTRACT
Fisher’s Renormalized Behaviour...................................... 356 4.2 Dynamic Critical Behaviour - Effects of the
System-asymmetry on Critical Dynamics.......................... 358
5 Conclusions................................................................................... 363
Glossary of Sym bols.......................................................................... 364
References............................................................................................. 367
1.1 Critical Behaviour of Fluids
As simple or binary fluids approach the critical points, the fluids exhibit the crossover from the classical mean-field to the three-dimensional Ising (3D Ising) behaviour. This static crossover indicates that the fluctuation of the order parameter (density or concentration) becomes infinitely large to become a dominant factor in thermodynamic behaviour. The critical behaviour is usually characterized by the critical exponents. In fluid systems, for example, the critical exponents 7 and v for the isothermal susceptibility S j and the correlation length £, are defined through the following equations
with the reduced temperature e = | Tj Ts — 11, where Ts is the temperature at the stability limit. S T0 and £/o are the respective critical amplitudes. At the crossover, the values of 7 and v vary from 7 = 1 and v = 1/2 to 7 = 1.24 and v = 0.63,1 respectively. The location of the crossover is characterized by the Ginzburg number Gi, which is a system-dependent parameter. Recently, Belyakov and Kiselev2,3 derived a simple universal function describing the static crossover of the isothermal susceptibility in terms of GU on the basis of a renormalization-group method with the ^-expansion.
