We study the behavior of a three-dimensional Ising-like system in an external field near the critical point by using the non-Gaussian spin-density fluctuations, namely, the quartic measure density with the even and odd powers of the variable ͑the asymmetric 4 model͒. The basic idea of the analytic method for deriving complete expressions of the thermodynamic characteristics ͑including the scaling functions͒ is described. The proposed method allows us to perform the calculations on the microscopic level without any adjustable parameters. Explicit expressions for the total free energy, order parameter, susceptibility, entropy, and specific heat of the system are obtained as functions of the temperature and field. The regions of the so-called weak and strong fields are considered for temperatures above and below T c ͑T c is the phase-transition temperature in the absence of an external field͒. The average spin moment and susceptibility, depending on the field variation and the proximity to T c , are investigated. It is confirmed that the temperature and field fluctuations for the order parameter play the leading roles in the weak and strong fields, respectively.

Correlation functions and transport coefficients of self-diffusion and shear viscosity of a binary Lennard-Jones mixture with components differing only in their particle mass are studied up to high values of the mass ratio µ, including the limiting case µ = ∞, for different mole fractions x. Within a large range of x and µ the product of the diffusion coefficient of the heavy species D2 and the total shear viscosity of the mixture ηm is found to remain constant, obeying a generalized Stokes-Einstein relation. At high liquid density, large mass ratios lead to a pronounced cage effect that is observable in the mean square displacement, the velocity autocorrelation function and the van Hove correlation function.

The description of a three-dimensional Ising-like magnet in the presence of an external field in the vicinity of the critical point by the collective variables method is proposed. Using the renormalization group transformations, the scaling region size is defined as a function of temperature and field. The obtained expressions for the free energy, equation of state and susceptibility allow one to analyse their dependence on microscopic parameters of the system. The critical exponents of the correlation length and order parameter are calculated as well. The results agree qualitatively with ones obtained within the framework of the parametric representation of the equation of state and Monte-Carlo simulations. The calculations do not involve any parametrization, phenomenological assumptions and adjustable parameters. The approach can be extended to models with a multicomponent order parameter.