Is the mean-field approximation so bad? A simple generalization yelding realistic critical indices for 3D Ising-class systems

Modification of the renormalization-group approach, invoking Stratonovich transformation at each step, is proposed to describe phase transitions in 3D Ising-class systems. The proposed method is closely related to the mean-field approximation. The low-order scheme works well for a wide thermal range, is consistent with a scaling hypothesis and predicts very reasonable values of critical indices.Comment: 4 page

Peculiarities in the behavior of the entropy diameter for molecular liquids as the reflection of molecular rotations and the excluded volume effects

The behavior of the diameter of the coexistence curve in terms of the entropy and the corresponding diameter are investigated. It is shown that the diameter of the coexistence curve in term of the entropy is sensitive to the change in the character of the rotational motion of the molecule in liquid phase which is governed by the short range correlations. The model of the compressible effective volume is proposed to describe the phase coexistence both in terms of the density and the entropy.Comment: 22 pages, 8 figures, 3 Table

New version of the fluctuation Hamiltonian for liquids near the critical point

We propose new canonical form of the fluctuational Hamiltonian which takes into account the fact that in the vicinity of the critical point there are two fluctuating fields. They are the field of the number density and the entropy. The proposed canonical form is based on the $D_5$ catastrophe. In contrast to the standard approach of Landau-Ginzburg Hamiltonian which is based on $A_3$ catastrophe the canonical form proposed for the fluctuational Hamiltonian naturally includes the asymmetric coupling between the fields.Comment: 15 page

Is the thermodynamic behavior of the noble fluids consistent with the Principle of Corresponding States?

The applicability of the Principle of Corresponding States (PCS) for the noble fluids is discussed. We give the thermodynamic evidences for the dimerization of the liquid phase in heavy noble gases like argon, krypton etc. which manifest itself in deviation from the PCS. The behavior of the rectilinear diameter of the entropy and the density is analyzed. It is shown that these characteristics are very sensitive to the dimerization process which takes place in the liquid phase of heavy noble gases.Comment: 23 pages, 11 figure

More is the Same; Phase Transitions and Mean Field Theories

This paper looks at the early theory of phase transitions. It considers a group of related concepts derived from condensed matter and statistical physics. The key technical ideas here go under the names of "singularity", "order parameter", "mean field theory", and "variational method". In a less technical vein, the question here is how can matter, ordinary matter, support a diversity of forms. We see this diversity each time we observe ice in contact with liquid water or see water vapor, "steam", come up from a pot of heated water. Different phases can be qualitatively different in that walking on ice is well within human capacity, but walking on liquid water is proverbially forbidden to ordinary humans. These differences have been apparent to humankind for millennia, but only brought within the domain of scientific understanding since the 1880s. A phase transition is a change from one behavior to another. A first order phase transition involves a discontinuous jump in a some statistical variable of the system. The discontinuous property is called the order parameter. Each phase transitions has its own order parameter that range over a tremendous variety of physical properties. These properties include the density of a liquid gas transition, the magnetization in a ferromagnet, the size of a connected cluster in a percolation transition, and a condensate wave function in a superfluid or superconductor. A continuous transition occurs when that jump approaches zero. This note is about statistical mechanics and the development of mean field theory as a basis for a partial understanding of this phenomenon.Comment: 25 pages, 6 figure