The influence of dimensional crossover on phase transitions and critical phenomena in condensed systems

This article is aimed at studying the effects of the dimensional crossover (DC) on physical properties of condensed systems near phase transition and critical points. Here we consider the following problems: (1) the theoretical provisions that allow to study the effect of spatial confinement on DC near phase transition and critical points; (2) the study of DC in condensed systems with the Ginzburg number Gi < 1, where fluctuation effects are described in different ways at the fluctuation, regular and intermediate (crossover) regions; (3) two types of DC were investigated: (a) a decrease in the linear dimensions L to the values of the correlation length of the order parameter fluctuations leads to the conversion of the dependence on thermodynamic variable into a dependence on linear sizes of 3D systems, as well as (b) a further decrease in linear sizes L the 3D–2D or 3D1D DC happens depending on slitlike or cylindrical geometry, which is determined by the value of the lower crossover dimensionality dLCD; (4) it is proposed to extend the known equalities for critical exponents by using the Mandelbrot formula for fractal dimension Df as a critical exponent; (5) the influence of 3D–2D DC on the characteristics of the fine structure of the molecular light scattering (MLS) spectrum is studied.